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V. I. Arnol’d (1997)
Mathematical Methods of Classical Mechanics
- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Dynamical Systems and Ergodic Theory
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/S1560354712060019
- Publisher site
- See Article on Publisher Site
Abstract
As we have proved in [11], the geodesic flows associated with the flat metrics on $$ \mathbb{T}^2 $$ minimize the polynomial entropy hpol. In this paper, we show that, among the geodesic flows that are Bott integrable and dynamically coherent, the geodesic flows associated with flat metrics are local strict minima for hpol. To this aim, we prove a graph property for invariant Lagrangian tori in near-integrable systems.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Dec 5, 2012