共查询到20条相似文献,搜索用时 93 毫秒
1.
In this paper we discuss a perturbed extension of hyperbolic twist mappings to a 3-dimensional measure-preserving mapping $$\begin{array}{*{20}c} {T:\left\{ {\begin{array}{*{20}c} {x_{n + 1} = s(x_n \cos \varphi _n - y_n \sin \varphi _n ) + A\cos z_n ,} \\ {y_{n + 1} = s^{ - 1} (x_n \sin \varphi _n + y_n \cos \varphi _n ) + B\sin z_n ,} \\ {z_{n + 1} = z_n + C\cos (x_{n + 1} + y_{n + 1} ) + D,(\bmod 2\pi )} \\ \end{array} } \right.} \\ {\varphi _n = (x_n^2 + y_n^2 )^k } \\ \end{array}$$ wheres, k are parameters andA, B, C, D are perturbation parameters. We find that the ordered regions near the fixed point of the hyperbolic twist mapping is destroyed by the perturbed extension more easily than the ones distant from it. The size of the ordered region decreases with increasing perturbation parameters and is insensitive to the parameterD for the same parametersA, B, C. 相似文献
2.
Yi-Sui Sun 《Celestial Mechanics and Dynamical Astronomy》1983,30(1):7-19
In this paper, using two methods: LCN'S (Lyapunov characteristic numbers) method and slice cutting method, we study numerically two mappings with odd dimension: $$T_1 :\left\{ {\begin{array}{*{20}c} {x_{n + 1} = x_n + z_n ,} \\ {y_{n + 1} = y_n + x_{n + 1} , (\bmod 2\pi )} \\ {z_{n + 1} = z_n + A\sin y_{n + 1} ,} \\ \end{array} } \right. T_2 :\left\{ {\begin{array}{*{20}c} {x_{n + 1} = x_n + y_n + B \sin z_n ,} \\ {y_{n + 1} = y_n + A \sin x_{n + 1} , (\bmod 2\pi ),} \\ {z_{n + 1} = z_n + B \sin y_{n + 1} ,} \\ \end{array} } \right.$$ whereA, B are parameters. For the mappingT 1 the whole region is stochastic; however, we find two-dimensional invariant manifolds for the mappingT 2. 相似文献
3.
Yi-Sui Sun 《Celestial Mechanics and Dynamical Astronomy》1985,37(2):171-181
We study an extension of the Hénon mapping to a dissipative dynamical system with three-dimensions and discuss the behavior of the attractors of the Hénon mapping in the extended mapping $$T:\left\{ {\begin{array}{*{20}c} {X_{i + 1} = Y_i + 1 - AX_i^2 + C cos Z_i } \\ {Y_{i + 1} = BX_i + D \sin Z_i } \\ {Z_{i + 1} = Z_i + E \sin Y_{i + 1} + F, (\bmod 2\pi ).} \\ \end{array} } \right.$$ The results show that the strange attractor is destroyed by perturbed extension more easily than the trivial attractor and the invariant manifold of the conservative dynamical system. 相似文献
4.
Two flights from Alice Springs, Australia, were achieved in November 1977 and November 1978 with a plastic scintillator -burst detector, effective area 6.3 m2, thickness 5 cm, energy response in the range 50 keV to 2 MeV. In 33 hr of good, high altitude data, two bursts were detected, yielding a rate corrected to an isotropic flux of
at a size of 8.5×10–9 erg cm–2. One event, seen at 22.14 on 15 Nov 1978, was confirmed by spacecraft measurements. The second, too small to be detected by spacecraft, arrived from 0 hr RA, –13.2° Decl. ±12° and possibly comes from a confirmed -burst source location. A galactic origin with a source distribution originating from a relatively thick disk, is favoured by these results. 相似文献
5.
Yi-Sui Sun 《Celestial Mechanics and Dynamical Astronomy》1984,33(2):111-125
In this paper, we study the following three-dimensional mappings $$T:\left\{ \begin{gathered} x_{n + 1} = x_n + y_n + B sin z_n , \hfill \\ y_{n + 1} = y_n + A sin x_{n + 1} , \hfill \\ z_{n + 1} = z_n + C sin y_{n + 1} + D, \hfill \\ \end{gathered} \right.\left( {\bmod 2\Pi } \right)$$ where A, B, C, D are parameters. When D>BC and 2π/D is an irrational number, we find numerically-two-dimensional and one-dimensional invariant manifolds, but when DBC and 2π/D is a rational number we find numerically one-dimensional manifolds and the fixed points for some cycles. 相似文献
6.
Boris Garfinkel 《Celestial Mechanics and Dynamical Astronomy》1973,8(2):207-212
If a dynamical problem ofN degress of freedom is reduced to the Ideal Resonance Problem, the Hamiltonian takes the form 1 $$\begin{array}{*{20}c} {F = B(y) + 2\mu ^2 A(y)\sin ^2 x_1 ,} & {\mu \ll 1.} \\ \end{array} $$ Herey is the momentum-vectory k withk=1,2?N, x 1 is thecritical argument, andx k fork>1 are theignorable co-ordinates, which have been eliminated from the Hamiltonian. The purpose of this Note is to summarize the first-order solution of the problem defined by (1) as described in a sequence of five recent papers by the author. A basic is the resonance parameter α, defined by 1 $$\alpha \equiv - B'/\left| {4AB''} \right|^{1/2} \mu .$$ The solution isglobal in the sense that it is valid for all values of α2 in the range 1 $$0 \leqslant \alpha ^2 \leqslant \infty ,$$ which embrances thelibration and thecirculation regimes of the co-ordinatex 1, associated with α2 < 1 and α2 > 1, respectively. The solution includes asymptotically the limit α2 → ∞, which corresponds to theclassical solution of the problem, expanded in powers of ε ≡ μ2, and carrying α as a divisor. The classical singularity at α=0, corresponding to an exact commensurability of two frequencies of the motion, has been removed from the global solution by means of the Bohlin expansion in powers of μ = ε1/2. The singularities that commonly arise within the libration region α2 < 1 and on the separatrix α2 = 1 of the phase-plane have been suppressed by means of aregularizing function 1 $$\begin{array}{*{20}c} {\phi \equiv \tfrac{1}{2}(1 + \operatorname{sgn} z)\exp ( - z^{ - 3} ),} & {z \equiv \alpha ^2 } \\ \end{array} - 1,$$ introduced into the new Hamiltonian. The global solution is subject to thenormality condition, which boundsAB″ away from zero indeep resonance, α2 < 1/μ, where the classical solution fails, and which boundsB′ away from zero inshallow resonance, α2 > 1/μ, where the classical solution is valid. Thedemarcation point 1 $$\alpha _ * ^2 \equiv {1 \mathord{\left/ {\vphantom {1 \mu }} \right. \kern-\nulldelimiterspace} \mu }$$ conventionally separates the deep and the shallow resonance regions. The solution appears in parametric form 1 $$\begin{array}{*{20}c} {x_\kappa = x_\kappa (u)} \\ {y_1 = y_1 (u)} \\ {\begin{array}{*{20}c} {y_\kappa = conts,} & {k > 1,} \\ \end{array} } \\ {u = u(t).} \\ \end{array} $$ It involves the standard elliptic integralsu andE((u) of the first and the second kinds, respectively, the Jacobian elliptic functionssn, cn, dn, am, and the Zeta functionZ (u). 相似文献
7.
Claude Froeschle 《Astrophysics and Space Science》1971,14(1):110-117
Dynamical systems with three degrees of freedom can be reduced to the study of a fourdimensional mapping. We consider here, as a model problem, the mapping given by the following equations: $$\left\{ \begin{gathered} x_1 = x_0 + a_1 {\text{ sin (}}x_0 {\text{ + }}y_0 {\text{)}} + b{\text{ sin (}}x_0 {\text{ + }}y_0 {\text{ + }}z_{\text{0}} {\text{ + }}t_{\text{0}} {\text{)}} \hfill \\ y_1 = x_0 {\text{ + }}y_0 \hfill \\ z_1 = z_0 + a_2 {\text{ sin (}}z_0 {\text{ + }}t_0 {\text{)}} + b{\text{ sin (}}x_0 {\text{ + }}y_0 {\text{ + }}z_{\text{0}} {\text{ + }}t_{\text{0}} {\text{) (mod 2}}\pi {\text{)}} \hfill \\ t_1 = z_0 {\text{ + }}t_0 \hfill \\ \end{gathered} \right.$$ We have found that as soon asb≠0, i.e. even for a very weak coupling, a dynamical system with three degrees of freedom has in general either two or zero isolating integrals (besides the usual energy integral). 相似文献
8.
F. P. Keenan 《Astrophysics and Space Science》1991,186(2):277-281
EinsteinA-coefficients for transitions inSii, calculated with the atomic structure package CIV3, are used to derive the electron density sensitive emission line ratio
相似文献
9.
V. G. Karetnikov 《Astrophysics and Space Science》1987,131(1-2):675-679
From the values of period changes for 6 close binary stars the mass transfer rate was calculated. Comparing these values Mt with the values of shell masses Msh, the expression $$lg \dot M_t = \begin{array}{*{20}c} {4.24} \\ { \pm 24} \\ \end{array} + \begin{array}{*{20}c} {0.63} \\ { \pm 6} \\ \end{array} lg M_{sh} $$ Was derived. The analysis of this expression points out the initial character of the outflow of matter, and one may determine the time interval of the substitution of the shell matter. So one may conclude that for a certain mass transfer rate, a certain amount of matter accumulates in the nearby regions of the system. The study of orbital period changes of close binary stellar systems led to the idea that these secular and irregular changes are due to the mass loss and to the redistribution of masses in a close binary. Secular changes of orbital periods are known for approximately 400 eclipsing binary stars. For many stars, including cataclysmic binaries, irregular period changes are known. Thus, the mass loss and the matter redistribution in close binaries are often observed phenomena. 相似文献
10.
From new observational material we made a curve of growth analysis of the penumbra of a large, stable sunspot. The analysis was done relative to the undisturbed photosphere and gave the following results (⊙ denotes photosphere, * denotes penumbra): $$\begin{gathered} (\theta ^ * - \theta ^ \odot )_{exe} = 0.051 \pm 0.007 \hfill \\ {{\xi _t ^ * } \mathord{\left/ {\vphantom {{\xi _t ^ * } {\xi _t }}} \right. \kern-\nulldelimiterspace} {\xi _t }}^ \odot = 1.3 \pm 0.1 \hfill \\ {{P_e ^ * } \mathord{\left/ {\vphantom {{P_e ^ * } {P_e ^ \odot = 0.6 \pm 0.1}}} \right. \kern-\nulldelimiterspace} {P_e ^ \odot = 0.6 \pm 0.1}} \hfill \\ {{P_g ^ * } \mathord{\left/ {\vphantom {{P_g ^ * } {P_g }}} \right. \kern-\nulldelimiterspace} {P_g }}^ \odot = 1.0 \pm 0.2 \hfill \\ \end{gathered} $$ The results of the analysis are in satisfactory agreement with the penumbral model as published by Kjeldseth Moe and Maltby (1969). Additionally we tested this model by computing the equivalent widths of 28 well selected lines and comparing them with our observations. 相似文献
11.
H. M. Srivástava 《Astrophysics and Space Science》1991,181(2):195-202
The multivariable hypergeometric function $$F_{q_0 :q_1 ;...;q_n }^{P_0 :P_1 ;...;P_n } \left( {\begin{array}{*{20}c} {x_1 } \\ \vdots \\ {x_n } \\ \end{array} } \right),$$ considered recently by A. W. Niukkanen and H.M. Srivastava, is known to provide an interesting unification of the generalized hypergeometric functionp F q of one variable, Appell and Kampé de Fériet functions of two variables, and Lauricella functions ofn variables, as also of many other hypergeometric series which arise naturally in various physical, astrophysical, and quantum chemical applications. Indeed, as already pointed out by Srivastava, this multivariable hypergeometric function is an obvious special case of the generalized Lauricella function ofn variables, which was first introduced and studied by Srivastava and M. C. Daoust. By employing such fruitful connections of this multivariable hypergeometric function with much more general multiple hypergeometric functions studied in the literature rather systematically and widely, Srivastava presented several interesting and useful properties of this function, most of which did not appear in the work of Niukkanen. The object of this sequel to Srivastava's work is to derive a further reduction formula for the multivariable hypergeometric function from substantially more general identities involving multiple series with essentially arbitrary terms. Some interesting connections of the results considered here with those given in the literature, and some indication of their applicability, are also provided. 相似文献
12.
A. K. Jain U. B. Jayanthi K. Kasturirangan U. R. Rao 《Astrophysics and Space Science》1973,21(1):107-116
The paper presents the intensity and spectral nature of the X-ray emission from Sco X-1 in the energy interval 17–106 keV based on the observations made by a balloon borne scintillation telescope system flown on November 15, 1971 from Hyderabad, India. In the 25–53 keV interval, the spectral distribution is observed to correspond to akT value of
keV assuming the shape to be exponential. Over the complete energy range of observation, a power law function with the value of exponent equal to 3.6±0.5 seems to yield an adequate fit. Comparing the present data with those obtained elsewhere, the temporal characteristics of the X-ray emission from Sco X-1 are discussed. 相似文献
13.
P. P. Hallan Sanjay Jain K. B. Bhatnagar 《Celestial Mechanics and Dynamical Astronomy》2000,77(3):157-184
The non-linear stability of L
4 in the restricted three-body problem has been studied when the bigger primary is a triaxial rigid body with its equatorial
plane coincident with the plane of motion. It is found that L
4 is stable in the range of linear stability except for three mass ratios:
14.
Stars are gravitationally stabilized fusion reactors changing their chemical composition while transforming light atomic nuclei into heavy ones. The atomic nuclei are supposed to be in thermal equilibrium with the ambient plasma. The majority of reactions among nuclei leading to a nuclear transformation are inhibited by the necessity for the charged participants to tunnel through their mutual Coulomb barrier. As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. Over the years various approaches have been made to derive closed-form representations of thermonuclear reaction rates (Critchfield, 1972; Haubold and John, 1978; Haubold, Mathai and Anderson, 1987). They show that the reaction rate contains the astrophysical cross section factor and its derivatives which has to be determined experimentally, and an integral part of the thermonuclear reaction rate independent from experimental results which can be treated by closed-form representation techniques in terms of generalized hypergeometric functions. In this paper mathematical/statistical techniques for deriving closed-form representations of thermonuclear functions, particularly the four integrals $$\begin{gathered} I_1 (z,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_2 (z,d,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_3 (z,t,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - z(y + 1)^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ I_4 (z,\delta ,b,v)\mathop = \limits^{def} \int\limits_0^\infty {y^v e^{ - y} e^{ - by^\delta } e^{ - zy^{ - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } dy,} \hfill \\ \end{gathered} $$ will be summarized and numerical results for them will be given. The separation of thermonuclear functions from thermonuclear reaction rates is our preferred result. The purpose of the paper is also to compare numerical results for approximate and closed-form representations of thermonuclear functions. This paper completes the work of Haubold, Mathai, and Anderson (1987). 相似文献
15.
Makhlouf Amar 《Celestial Mechanics and Dynamical Astronomy》1991,52(4):397-406
We consider the Hill's equation: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca% WGKbWaaWbaaSqabeaacaaIYaaaaOGaeqOVdGhabaGaamizaiaadsha% daahaaWcbeqaaiaaikdaaaaaaOGaey4kaSYaaSaaaeaacaWGTbGaai% ikaiaad2gacqGHRaWkcaaIXaGaaiykaaqaaiaaikdaaaGaam4qamaa% CaaaleqabaGaaGOmaaaakiaacIcacaWG0bGaaiykaiabe67a4jabg2% da9iaaicdaaaa!4973!\[\frac{{d^2 \xi }}{{dt^2 }} + \frac{{m(m + 1)}}{2}C^2 (t)\xi = 0\]Where C(t) = Cn (t, {frbuilt|1/2}) is the elliptic function of Jacobi and m a given real number. It is a particular case of theame equation. By the change of variable from t to defined by: % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaOWaaiqaaq% aabeqaamaalaaajaaybaGaamizaGGaaiab-z6agbqaaiaadsgacaWG% 0baaaiabg2da9OWaaOaaaKaaGfaacaGGOaqcKbaG-laaigdajaaycq% GHsislkmaaleaajeaybaGaaGymaaqaaiaaikdaaaqcaaMaaeiiaiaa% bohacaqGPbGaaeOBaOWaaWbaaKqaGfqabaGaaeOmaaaajaaycqWFMo% GrcqWFPaqkaKqaGfqaaaqcaawaaiab-z6agjab-HcaOiab-bdaWiab% -LcaPiab-1da9iab-bdaWaaakiaawUhaaaaa!51F5!\[\left\{ \begin{array}{l}\frac{{d\Phi }}{{dt}} = \sqrt {(1 - {\textstyle{1 \over 2}}{\rm{ sin}}^{\rm{2}} \Phi )} \\\Phi (0) = 0 \\\end{array} \right.\]it is transformed to the Ince equation: (1 + · cos(2)) y + b · sin(2) · y + (c + d · cos(2)) y = 0 where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaqcaawaaiaadggacq% GH9aqpcqGHsislcaWGIbGaeyypa0JcdaWcgaqaaiaaigdaaeaacaaI% ZaGaaiilaiaabccacaWGJbGaeyypa0Jaamizaiabg2da9aaacaqGGa% WaaSaaaKaaGfaacaWGTbGaaiikaiaad2gacqGHRaWkcaaIXaGaaiyk% aaqaaiaaiodaaaaaaa!4777!\[a = - b = {1 \mathord{\left/{\vphantom {1 {3,{\rm{ }}c = d = }}} \right.\kern-\nulldelimiterspace} {3,{\rm{ }}c = d = }}{\rm{ }}\frac{{m(m + 1)}}{3}\]In the neighbourhood of the poles, we give the expression of the solutions.The periodic solutions of the Equation (1) correspond to the periodic solutions of the Equation (3). Magnus and Winkler give us a theory of their existence. By comparing these results to those of our study in the case of the Hill's equation, we can find the development in Fourier series of periodic solutions in function of the variable and deduce the development of solutions of (1) in function of C(t). 相似文献
16.
P. Vivekananda Rao M. B. K. Sarma B. V. N. S. Prakash Rao 《Journal of Astrophysics and Astronomy》1991,12(3):225-263
Results of analysis of photoelectric observations of the RS CVn eclipsing binary WY Cancri in the standard passbands ofUBV during 1973-74, 1976-79 and inUBVRI during 1984-86 are reported. A preliminary analysis of the eclipses suggested the primary eclipse to be transit. A study
of the percentage contribution of the distortion wave amplitudes in all the colours with respect to the luminosities of both
components, showed the hotter component to be the source of the distortion wave. The clean (wave removed) light curves of
different epochs have not merged, suggesting residual effects of spot activity. The reason for this is attributed to the presence
of either (1) polar spots or (2) small spots uniformly distributed all over the surface of the hotter component. This additional
variation is found to have a periodicity of about 50 years or more. The distortion waves in yellow colour are modelled according
to Budding’s (1977) method. For getting the best fit of the observations and theory, it was found necessary to assume three
or four spots on the surface of the hot component. Out of these four spot groups, three are found to have direct motion with
migration periods of 1.01, 1.01 and 2.51 years while the fourth one has a retrograde motion with a migration period of 3.01
years. From these periods and the latitudes of the spots derived from the model a co-rotating latitude of 4ℴ is obtained.
The temperatures of these spots are found to be lower than that of the photosphere by about 700ℴK to 800ℴK. Assuming the light
curve of 1985-86, which is the brightest of all the observed seasons, to be least affected by the spots, the light curves
of the other seasons are all brought up to the quadrature level of this season by applying suitable corrections. The merged
curves in theUBVRI colours are analysed for the elements by the Wilson-Devinney method. This analysis yielded the following absolute elements:
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