A note on the volume flux of smooth and continuous strictly contact\n isotopies

2011/07/25 by Stefan Müller, Stefan C. Müller, Müller, Stefan
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #53D35 #Astro and Planetary Science #FOS: Mathematics #Geology and Paleoclimatology Research #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1107.4869

openalex publication_date 2011/07/25 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

This note on the flux homomorphism for strictly contact isotopies complements\nthe recent paper [MS11a] by P. Spaeth and the author. We determine the volume\nflux restricted to symplectic and volume-preserving contact isotopies and their\nC⁰-limits for some classes of symplectic and contact manifolds and for a\nnumber of examples. In particular, we see that the restriction of the flux may\nfail to be surjective. It vanishes for an isotopy preserving a regular contact\nform, but can be nontrivial for non-regular contact forms. Applications are\ndiscussed in the article cited above. We also find obstructions to regularizing\na strictly contact isotopy that are not present for Hamiltonian isotopies\n[Pol01, Section 5.2] or contact isotopies [MS11b].\n

Related

• Uniqueness of contact Hamiltonians of topological strictly contact isotopies
• An obstruction to conservation of volume in contact dynamics
• Topological contact dynamics I: symplectization and applications of the\n energy-capacity inequality
• Topological contact dynamics III: uniqueness of the topological\n Hamiltonian and C⁰-rigidity of the geodesic flow
• Extending the flux homomorphism to volume-preserving homeomorphisms