Vanishing of the entropy pseudonorm for certain integrable systems

DOI10.1090/S1079-6762-06-00156-9zbMath1186.37067OpenAlexW1530901505MaRDI QIDQ3432104

Vladimir S. Matveev, Boris S. Kruglikov

Publication date: 13 April 2007

Published in: Electronic Research Announcements of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1079-6762-06-00156-9

zbMATH Keywords

1-parameter subgroup of the abelian group of flowscompletely integrable Benenti systemVanishing of topological entropy

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Topological entropy (37B40)

Related Items (5)

Quantum integrability for the Beltrami-Laplace operators of projectively equivalent metrics of arbitrary signatures ⋮ Integrable systems and group actions ⋮ Proof of the projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two ⋮ Complete Einstein metrics are geodesically rigid ⋮ Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta

Cites Work

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• Invariant fibrations of geodesic flows
• Normal forms for Hamiltonian systems with Poisson commuting integrals - elliptic case
• Trajectory equivalence and corresponding integrals
• Geodesic flows
• On the topology of manifolds with completely integrable geodesic flows. II
• Three-dimensional manifolds having metrics with the same geodesics.
• Hyperbolic manifolds are geodesically rigid
• Integrable geodesic flows with positive topological entropy
• Action-angle coordinates at singularities for analytic integrable systems
• Examples of integrable sub-Riemannian geodesic flows
• Collective geodesic flows.
• Geometrical interpretation of Benenti systems
• Projectively equivalent metrics on the torus
• Topological entropy of group and semigroup actions
• Bihamiltonian structures and Stäckel separability
• Special symmetric two-tensors, equivalent dynamical systems, cofactor and bi-cofactor systems
• Zero entropy and bounded topology
• Bi-differential calculi, bi-Hamiltonian systems and conformal Killing tensors
• Some ergodic properties of commuting diffeomorphisms
• On the topology of manifolds with completely integrable geodesic flows
• On collective complete integrability according to the method of Thimm
• Driven Newton equations and separable time-dependent potentials
• Entropy for Group Endomorphisms and Homogeneous Spaces
• [https://portal.mardi4nfdi.de/wiki/Publication:5676460 Entropie d'un groupe ab�lien de transformations]

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