Riemannian theory of Hamiltonian chaos and Lyapunov exponents
نویسندگان
چکیده
منابع مشابه
Riemannian theory of Hamiltonian chaos and Lyapunov exponents.
A non-vanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system, however no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ε = E/N , the energy per degree of freedom. The fu...
متن کاملMathematical theory of Lyapunov exponents
This paper reviews some basic mathematical results on Lyapunov exponents, one of the most fundamental concepts in dynamical systems. The first few sections contain some very general results in nonuniform hyperbolic theory. We consider ( f , μ), where f is an arbitrary dynamical system and μ is an arbitrary invariant measure, and discuss relations between Lyapunov exponents and several dynamical...
متن کاملChaos and Lyapunov exponents in classical and quantal distribution dynamics
We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions r(p ,q). Of particular interest is l2 , an exponent that quantifies the rate at which chaotically evolving distributions acquire structure at increasingly smaller scales and is generally larger than the maximal Lyapunov exponent l for trajectories. The approach is trajectory inde...
متن کاملLyapunov Exponents and Smooth Ergodic Theory
This book provides a systematic introduction to smooth ergodic theory, including the general theory of Lyapunov exponents, nonuniform hyperbolic theory, stable manifold theory emphasizing absolute continuity of invariant foliations, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents. The book can be used as a primary textbook for a special topics course on nonuniform hy...
متن کاملThe bootstrap and Lyapunov exponents in deterministic chaos
Inasmuch as Lyapunov exponents provide a necessary condition for chaos in a dynamical system, confidence bounds on estimated Lyapunov exponents are of great interest. Estimates derived either from observations or from numerical integrations are limited to trajectories of finite length, and it is the uncertainties in (the distribution of) these finite time Lyapunov exponents which are of interes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 1996
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.54.5969