The contact property for magnetic flows on surfaces

TL;DR

This thesis investigates the contact properties of magnetic flows on surfaces, computing symplectic homology at extreme energy levels and analyzing dynamical convexity in symmetric cases, advancing understanding of magnetic dynamical systems.

Contribution

It computes symplectic homology for magnetic systems on surfaces at extreme energies and establishes dynamical convexity for symmetric magnetic flows.

Findings

Symplectic homology computed for very large or small energies.

Dynamical convexity established for low energy symmetric magnetic flows.

Analysis of contact properties enhances understanding of magnetic flow dynamics.

Abstract

This is the author's PhD Thesis (University of Cambridge, 2014) in its original form. In the first part, using an invariance result, we compute the symplectic homology of contact-type energy levels for magnetic systems on surfaces, provided the energy is very large or very small. In the second part, which is partially contained in the later paper (Benedetti, Ergod. Theory Dynam. Syst., 2016), we discuss some rotationally symmetric examples and establish dynamical convexity for symplectic magnetic flows on low energy levels.