Connecting orbits for families of Tonelli Hamiltonians

Vito Mandorino

doi:10.3934/jmd.2012.6.499

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2012, Volume 6, Issue 4: 499-538. Doi: 10.3934/jmd.2012.6.499

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Connecting orbits for families of Tonelli Hamiltonians

Vito Mandorino^1,

1.
Université Paris-Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16

Received: April 30, 2012

Published: December 2012

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Abstract

We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the time-one maps of a family of Tonelli Hamiltonians. Such systems are known as 'polysystems' or 'iterated function systems'. When specialized to families of twist maps on the cylinder, our results are similar to those obtained by Moeckel [20] and Le Calvez [15]. Our approach is based on weak KAM theory and is close to the one used by Bernard in [3] to study the case of a single Tonelli Hamiltonian.

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Mathematics Subject Classification: Primary: 37J50, 37J45; Secondary: 37J40, 70Hxx.

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References

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