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This article is cited in 19 scientific papers (total in 19 papers)
Flat Metrics are Strict Local Minimizers for the Polynomial Entropy
Clémence Labrousse Institut de Mathématiques de Jussieu, UMR 7586, Analyse algébrique, 175 rue du Chevaleret, 75013 Paris, France
Abstract:
As we have proved in [11], the geodesic flows associated with the flat metrics on $\mathbb{T}^2$ minimize the polynomial entropy $h_{pol}$. 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 $h_{pol}$. To this aim, we prove a graph property for invariant Lagrangian tori in near-integrable systems.
Keywords:
geodesic flows, polynomial entropy, integrable systems.
Received: 12.09.2012 Accepted: 28.09.2012
Citation:
Clémence Labrousse, “Flat Metrics are Strict Local Minimizers for the Polynomial Entropy”, Regul. Chaotic Dyn., 17:6 (2012), 479–491
Linking options:
https://www.mathnet.ru/eng/rcd416 https://www.mathnet.ru/eng/rcd/v17/i6/p479
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