Holomorphic Differentials, Thermostats and Anosov flows

Thomas Mettler

Institut für Mathematik, Goethe-Universität Frankfurt, Frankfurt am Main, Germany

Gabriel P. Paternain

Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, England

Date: May 18, 2018

Published Version: Math. Ann. 373 (2019), 553—580

2 Preliminaries on general thermostats

2.1 Jacobi equations

2.2 Quotient cocycle

2.3 Infinitesimal generators and conjugate cocycles

3 Dominated splitting and hyperbolicity for thermostats

5 The case of holomorphic differentials

5.1 Anosov flows

5.2 Dissipation and volume

6 The cases \(m=2\) and \(m=3\)

6.1 The case \(m=2\)

6.2 The case \(m=3\)

7 Regularity of weak foliations

8 The path geometry defined by a thermostat