On conformal points of area preserving maps and related topics

Peter Albers, Serge Tabachnikov

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we consider area preserving diffeomorphisms of planar domains, and we are interested in their conformal points, i.e., points at which the derivative is a similarity. We present some conditions that guarantee existence of conformal points for the infinitesimal problem of Hamiltonian vector fields as well as for what we call moderate symplectomorphisms of simply connected domains. We also link this problem to the Carathéodory and Loewner conjectures.

Original languageEnglish (US)
Article number104644
JournalJournal of Geometry and Physics
Volume180
DOIs
StatePublished - Oct 2022

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • General Physics and Astronomy
  • Geometry and Topology

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