Topological contact dynamics III: uniqueness of the topological\n Hamiltonian and C⁰-rigidity of the geodesic flow

2013/05/29 by Stefan C. Müller, Müller, Stefan, Peter Spaeth +1
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1305.6951

Abstract

We prove that a topological contact isotopy uniquely defines a topological\ncontact Hamiltonian. Combined with previous results from [MS11], this\ngeneralizes the classical one-to-one correspondence between smooth contact\nisotopies and their generating smooth contact Hamiltonians and conformal\nfactors to the group of topological contact dynamical systems. Applications of\nthis generalized correspondence include C⁰-rigidity of smooth contact\nHamiltonians, a transformation law for topological contact dynamical systems,\nand C⁰-rigidity of the geodesic flows of Riemannian manifolds.\n

Related

• Topological contact dynamics I: symplectization and applications of the\n energy-capacity inequality
• Topological contact dynamics II: topological automorphisms, contact\n homeomorphisms, and non-smooth contact dynamical systems
• Geodesic flows and contact toric manifolds
• Rigidity in topological dynamics
• Uniqueness of contact Hamiltonians of topological strictly contact isotopies