Proof of the index conjecture in Hofer geometry

DOI10.4310/MRL.2013.V20.N5.A13zbMATH Open1295.53089arXiv1204.3098WikidataQ123344907 ScholiaQ123344907MaRDI QIDQ2510102

Yasha Savelyev

Publication date: 31 July 2014

Published in: Mathematical Research Letters (Search for Journal in Brave)

Abstract: Let $gamma$ be a non-degenerate Ustilovsky geodesic in $Ham(M,omega)$ generated by $H$. We give a simple proof of a generalization of the conjecture stated in cite{virtmorse}, relating the Morse index of $gamma$, as a critical point of the Hofer length functional, with the Conley Zehnder index of the extremizers of $H$, considered as periodic orbits.

Full work available at URL: https://arxiv.org/abs/1204.3098

zbMATH Keywords

Hofer length functionalConley Zehnder indexUstilovsky geodesic

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Index theory for dynamical systems, Morse-Conley indices (37B30) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

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