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Article Dans Une Revue Annales Henri Lebesgue Année : 2021

ORBIT GROWTH OF CONTACT STRUCTURES AFTER SURGERY

CROISSANCE DES ORBITES PÉRIODIQUES ET COMPLEXITÉ POUR DES STRUCTURES DE CONTACT CONSTRUITES PAR CHIRURGIE

Résumé

This work is at the intersection of dynamical systems and contact geometry, and it focuses on the effects of a contact surgery adapted to the study of Reeb fields and on the effects of invariance of contact homology. We show that this contact surgery produces an increased dynamical complexity for all Reeb flows compatible with the new contact structure. We study Reeb Anosov fields on closed 3manifolds that are not topologically orbit-equivalent to any algebraic flow; this includes many examples on hyperbolic 3-manifolds. Our study also includes results of exponential growth in cases where neither the flow nor the manifold obtained by surgery is hyperbolic, as well as results when the original flow is periodic. This work fully demonstrates, in this context, the relevance of contact homology to the analysis of the dynamics of Reeb fields.
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Dates et versions

hal-03132118 , version 1 (04-02-2021)

Identifiants

  • HAL Id : hal-03132118 , version 1

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Patrick Foulon, Boris Hasselblatt, Anne Vaugon. ORBIT GROWTH OF CONTACT STRUCTURES AFTER SURGERY. Annales Henri Lebesgue, In press. ⟨hal-03132118⟩
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