Brandenbursky, Michael and Marcinkowski, Michal (2019) ENTROPY AND QUASIMORPHISMS. JOURNAL OF MODERN DYNAMICS, 15. pp. 143-163. ISSN 1930-5311, 1930-532X
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Let S be a compact oriented surface. We construct homogeneous quasimorphisms on Diff(S, area), on Diff(0)(S, area), and on Ham(S), generalizing the constructions of Gambaudo-Ghys and Polterovich. We prove that there are infinitely many linearly independent homogeneous quasimorphisms on Diff(S, area), on Diff(0)(S, area), and on Ham(S) whose absolute values bound from below the topological entropy. In cases when S has a positive genus, the quasimorphisms we construct on Ham(S) are C-0-continuous. We define a bi-invariant metric on these groups, called the entropy metric, and show that it is unbounded. In particular, we reprove the fact that the autonomous metric on Ham(S) is unbounded.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DIFFEOMORPHISMS; GEOMETRY; FLOWS; Area-preserving and Hamiltonian diffeomorphisms; topological entropy; quasimorphisms; braid groups; mapping class groups; conjugation-invariant norms |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 27 Apr 2020 09:53 |
| Last Modified: | 27 Apr 2020 09:53 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27783 |
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