Titlebook: Construction of Mappings for Hamiltonian Systems and Their Applications; Sadrilla S. Abdullaev Book 2006 Springer-Verlag Berlin Heidelberg

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Ungleiche Netzwerke - Vernetzte UngleichheitIn this chapter we study the statistical properties of chaotic motion in a stochastic layer in the context of their relation with the structure of phase space near saddle points. Before discussing this problem we briefly recall the statistical methods of description of chaotic transport in a stochastic layer of dynamical systems.

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0075-8450 electromagnetism.Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical proble

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https://doi.org/10.1007/978-3-531-92140-2 due to the exponential divergence of orbits with close initial conditions. This phenomenon creates the zone of phase space in the small vicinity of the unperturbed separatrix, so-called a . where the motion of system is chaotic (see Sect. 7.1.3).

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Klaus-Ove Kahrmann,Peter Bendixen and the phase space coordinates (.) → (λ., λ.). The rescaling parameter . depends only on the frequency of perturbation, ., and the divergence exponent . of unperturbed orbits near the saddle point, . = exp(2.). It means that the topology of phase space near the saddle point is a periodic function of log . with the certain period, log ..

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Rescaling Invariance of Hamiltonian Systems Near Saddle Points, and the phase space coordinates (.) → (λ., λ.). The rescaling parameter . depends only on the frequency of perturbation, ., and the divergence exponent . of unperturbed orbits near the saddle point, . = exp(2.). It means that the topology of phase space near the saddle point is a periodic function of log . with the certain period, log ..