Title: Dynamical complexity and symplectic integrability
Abstract:We introduce two numerical conjugacy invariants for systems -- the
complexity and weak complexity indices -- which are well-suited for the study
of completely Hamiltonian systems. These invariants can...We introduce two numerical conjugacy invariants for systems -- the
complexity and weak complexity indices -- which are well-suited for the study
of completely Hamiltonian systems. These invariants can be seen as
slow entropies, they describe the polynomial growth rate of the number of
balls (for the usual dynamical distances) of coverings of the ambient space.
We then define a new class of integrable systems, which we call decomposable
systems, for which one can prove that the weak complexity index is smaller than
the number of degrees of freedom. Hamiltonian systems integrable by means of
non-degenerate integrals (in Eliasson-Williamson sense), subjected to natural
additional assumptions, are the main examples of decomposable systems. We
finally give explicit examples of computation of the complexity index, for
Morse Hamiltonian systems on surfaces and for two-dimensional gradient systems.Read More
Publication Year: 2016
Publication Date: 2016-06-12
Language: en
Type: preprint
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