Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level

Alberto Abbondandolo; Leonardo Macarini; Marco Mazzucchelli; Gabriel P. Paternain

doi:10.4171/jems/674

JournalsjemsVol. 19, No. 2pp. 551–579

Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level

Alberto Abbondandolo
Universität Bochum, Germany
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- zbMATH Open
Leonardo Macarini
Universidade Federal do Rio de Janeiro, Brazil
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- zbMATH Open
Marco Mazzucchelli
Université de Lyon, France
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- ORCID
Gabriel P. Paternain
University of Cambridge, UK
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- zbMATH Open

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Abstract

We consider an exact magnetic ow on the tangent bundle of a closed surface. We prove that for almost every energy level $κ$ below the Mañé critical value of the universal covering there are infinitely many periodic orbits with energy $κ$ .

Cite this article

Alberto Abbondandolo, Leonardo Macarini, Marco Mazzucchelli, Gabriel P. Paternain, Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level. J. Eur. Math. Soc. 19 (2017), no. 2, pp. 551–579

DOI 10.4171/JEMS/674