Abstract:
We introduce two numerical conjugacy invariants of dynamical systems — the polynomial entropy and the weak polynomial entropy — which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants describe the polynomial growth rate of the number of balls (for the usual "dynamical" distances) of covers of the ambient space. We give explicit examples of computation of these polynomial entropies for generic Hamiltonian systems on surfaces.
The preparation of this paper was motivated and made possible by the rich interaction initiated by the ANR Intégrabilité réelle et complexe en Mécanique Hamiltonienne (JC0541465).
\Bibitem{Mar13}
\by Jean-Pierre Marco
\paper Polynomial Entropies and Integrable Hamiltonian Systems
\jour Regul. Chaotic Dyn.
\yr 2013
\vol 18
\issue 6
\pages 623--655
\mathnet{http://mi.mathnet.ru/rcd153}
\crossref{https://doi.org/10.1134/S1560354713060051}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3146583}
\zmath{https://zbmath.org/?q=an:1286.70022}
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