Integrable geodesic flow with positive topological entropy

Abstract

An example of a real-analytic metric on a compact manifold whose geodesic flow is Liouville integrable by $C^{\infty }$ functions and has positive topological entropy is constructed.

7 pages, LaTeX

Cited by in corpus (27)

• Symmetries and Integrability
• Polynomial growth of volume of balls for zero-entropy geodesic systems
• Integrable geodesic flows on the suspensions of toric automorphisms
• Jacobi-Maupertius metric and Kepler equation
• Spectra of Sol-manifolds: arithmetic and quantum monodromy
• The geodesic flow on nilmanifolds
• Invariant fibration of geodesic flows
• Magnetic flows on Sol-manifolds: dynamical and symplectic aspects
• Tonelli Hamiltonians without conjugate points and $C^0$ integrability
• Closed manifolds admitting metrics with the same geodesics
• On Local Description of Two-Dimensional Geodesic Flows with a Polynomial First Integral
• A few things I learnt from Jurgen Moser
• Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application
• Chaos and integrability in SL(2,R)-geometry
• Homogeneity of magnetic trajectories in the real special linear group
• Homogeneity of magnetic trajectories in the Berger sphere
• Positive-Entropy Integrable Systems and the Toda Lattice, II
• Symbolic dynamics for the anisotropic $N$-centre problem at negative energies
• Regularity and convergence of local first integrals of analytic differential systems
• Laplacian and spectral gap in regular Hilbert geometries
• On the non-integrability and dynamics of discrete models of threads
• The Spheres of Sol
• Deformational rigidity of integrable metrics on the torus
• Dynamical complexity and symplectic integrability
• Quantum Bianchi-VII problem, Mathieu functions and arithmetic
• First integrals on step-two and step-three nilpotent Lie groups
• About analytic non integrability