Flat metrics are strict local minimizers for the polynomial entropy

DOI10.1134/S1560354712060019zbMath1264.53077arXiv1207.4934WikidataQ125662211 ScholiaQ125662211MaRDI QIDQ1941918

Clémence Labrousse

Publication date: 22 March 2013

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4934

zbMATH Keywords

integrable systemsgeodesic flowpolynomial entropy

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Global Riemannian geometry, including pinching (53C20) Geodesic flows in symplectic geometry and contact geometry (53D25)

Related Items (15)

An entropic characterization of the flat metrics on the two torus ⋮ Polynomial entropy of amenable group actions for noncompact sets ⋮ Polynomial entropy of Morse-Smale diffeomorphisms on surfaces ⋮ Polynomial entropy of induced maps of circle and interval homeomorphisms ⋮ Variational principle for polynomial entropy on subsets of free semigroup actions ⋮ Polynomial entropy of subsets for free semigroup actions ⋮ Polynomial entropy and expansivity ⋮ Open problems in the theory of finite-dimensional integrable systems and related fields ⋮ Automorphisms of compact Kähler manifolds with slow dynamics ⋮ Entropy of billiard maps and a dynamical version of the Birkhoff conjecture ⋮ Categorical polynomial entropy ⋮ Polynomial entropies for Bott integrable Hamiltonian systems ⋮ Polynomial entropy of nonautonomous dynamical systems for noncompact sets ⋮ Slow volume growth for Reeb flows on spherizations and contact Bott–Samelson theorems ⋮ Scaled entropy for dynamical systems

Cites Work

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• Topological entropy for geodesic flows
• Riemannian tori without conjugate points are flat
• Entropy and rigidity of locally symmetric spaces of strictly negative curvature
• Four applications of conformal equivalence to geometry and dynamics
• Entropy and Completely Integrable Hamiltonian Systems
• Minimal entropy and Mostow's rigidity theorems

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