Theoretical Computation of Lyapunov Exponents for Almost Periodic Hamiltonian Systems
نویسنده
چکیده
Lyapunov exponents are an important concept to describe qualitative properties of dynamical systems. For instance, chaotic systems can be caracterized with the positivity of the largest Lyapunov exponent. In this paper, we use the Iwasawa decomposition of the semisimple Lie group Sp(n,R) and the enlargement of the phase space to give a theoretical computation of Lyapunov exponents of almost periodic Hamiltonian systems. In particular, we obtain the existence of Lyapunov exponents everywhere in the surface of constant energy of the Hamiltonian H . It turns out that, in this context, the Oseledec’s assumption is not necessary to guarantee the existence and the finitness of Lyapunov exponents.
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