Sommario
Questo articolo, insieme con il precedente (Parte 1: Teoria, pubblicato in questa stessa rivista) è inteso a fornire un metodo esplicito per il calcolo di tutti gli esponenti caratteristici di Lvapunov per un sistema dinamico. Dopo la teoria generale su tali esponenti sviluppata nella prima parte, qui si illustra il metodo di calcolo (Capitolo A) e si danno esempi numerici per applicazioni di varietà in sè e per sistemi Hamiltoniani (Capitolo B).
Summary
The present paper, together with the previous one (Part 1: Theory, published in this journal) is intended to give an explicit method for computing all Lyapunov Characteristic Exponents of a dynamical system. After the general theory on such exponents developed in the first part, in the present paper the computational method is described (Chapter A) and some numerical examples for mappings on manifolds and for Hamiltonian systems are given (Chapter B).
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References
Benettin G., Galgani L. andStrelcyn J.-M.,Kolmogorov Entropy and Numerical Experiments, Phys. Rev.A14, p. 2338–2345, 1976.
Benettin G. andStrelcyn J.-M.,Numerical Experiments on the Free Motion of a Point Mass Moving in a Plane Convex Region: Stochastic Transition and Entropy, Phys. Rev.A17, p. 773–785, 1978.
Contopouos G., Galgani L. andGiorgilli A.,On the Number of Isolating Integrals for Hamiltonian Systems,Phys. Rev. A18, p. 1183–1189, 1978.
Benettin G., Galgani L., Giorgilli A. andStrelcyn J.-M.,Tous les Nombres Caractéristiques de Lyaponov sont effectivement calculables, C.R. Acad. Sc. Paris, 286A, p. 431–433, 1978.
Benettin G., Galgani L., Giorgilli A. andStrelcyn J.-M.,Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems; a Method for Computing all of them. Part I: Theory, Meccanica
Benettin G., Casartelli M., Galgani L., Giorgilli A. andStrelcyn J.-M.,On the Reliability of Numerical Studies of Stochasticity. Part I: Existence of Time Averages,Nuovo Cimento 44B, p. 183–195, 1978.
Benettin G., Casartelli M., Galgani L., Giorgilli A. andStrelcyn J.-M.,On the Reliability of Numerical Studies of Stochasticity, Part II: Identification of Time Averages, Nuovo Cimento50B, p. 211–232, 1979.
Lorenz E. N.,Deterministic Nonperiodic Flow, J. Atmospheric Sciences20, p. 130–141, 1963.
Lanford O. E.,Qualitative and Statistical Theory of Dissipative Systems, inGallavotti G. (ed.),Statistical Mechanics, Liguori, Napoli, 1978.
Henon M.,A Two-dimensional Mapping with a Strange Attractor, Commun. math. Phys.50, 69–77, 1976.
Nagashima T. andShimada I.,On the C-System-Like Property of the Lorenz System, Progress of Theor. Phys.58, p. 1318–1319, 1977.
Feit S.D.,Characteristic Exponents and Strange Attractors, Commun. Math. Phys.61, p. 249–260, 1978.
Ruelle D.,Dynamical Systems with Turbulent Behaviour, IHES preprint, 1977.
Ruelle D.,On the Mesaures which describe Turbulence, IHES preprint 1978.
Froeschle C.,A Numerical Study of the Stochasticity of Dynamical Systems with two Degrees of Freedom, Astron. and Astrophys.9, p. 15–23, 1970.
Froeschle C.,Numerical Study of a Four-Dimensional Mapping, Astron. and Astrophys. 16, p. 172 – 189, 1972.
Froeschle C. andScheidecker J. P.,Numerical Study of the Stochasticity of Dynamical Systems with more than two Degrees of Freedom, Journal of Comput. Phys.11, p. 423–439, 1973.
Froeschle C. andScheidecker J. P.,Numerical Study of a four Dimensional Mapping II, Astron. and Astrophys.22, p. 431–436, 1973.
Froeschle C. andScheidecker J.P.,On the Disappearence of Isolating Integrals in Dynamical Systems with more than two Degrees of Freedom, inKozai Y. (ed.) —The stability of the Solar System and Small Stellar Systems (IAU 1974). Published also in Astrophysics and Space Science25, p. 373 – 386, 1973.
Froeschle C.,Numerical Study of a Random Dynamical System with two Degrees of Freedom, Astrophysics and Space Science37, p. 87–100, 1975.
Froeschle C.,Connectance of Dynamical Systems with Increasing Number of Degrees of Freedom, Phys. Rev.A18, p. 277–281, 1978
Henon M. andHeiles C.,The Applicability of the Third Integral of Motion: Some Numerical Experiments, Astron. Journal69, p. 73–79, 1964.
Carotta M. C., Ferrario C., Lo Vecchio G. andGalgani L.,New Phenomenon in the Stochastic Transition of Coupled Oscillators, Phys. Rev.A17, p. 786–794, 1978.
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Benettin, G., Galgani, L., Giorgilli, A. et al. Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application. Meccanica 15, 21–30 (1980). https://doi.org/10.1007/BF02128237
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DOI: https://doi.org/10.1007/BF02128237