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The $C^{0}$ integrability of symplectic twist maps without conjugate points

Published online by Cambridge University Press:  15 August 2019

MARC ARCOSTANZO*
Affiliation:
Laboratoire de Mathématiques d’Avignon (EA2151), Avignon Université, France email [email protected]

Abstract

It is proved that a symplectic twist map of the cotangent bundle $T^{\ast }\mathbb{T}^{d}$ of the $d$-dimensional torus that is without conjugate points is $C^{0}$-integrable, that is  $T^{\ast }\mathbb{T}^{d}$ is foliated by a family of invariant $C^{0}$ Lagrangian graphs.

Type
Original Article
Copyright
© Cambridge University Press, 2019

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