Generic Hamiltonian Dynamics

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Abstract

In this paper we contribute to the generic theory of Hamiltonians by proving that there is a \(C^2\)-residual \({\mathcal {R}}\) in the set of \(C^2\) Hamiltonians on a closed symplectic manifold \(M\), such that, for any \(H\in {\mathcal {R}}\), there is a full measure subset of energies \(e\) in \(H(M)\) such that the Hamiltonian level \((H,e)\) is topologically mixing; moreover these level sets are homoclinic classes.

Keywords

Hamiltonian vector field Topological transitivity Topological mixing Pseudo-orbits 

Mathematics Subject Classification

Primary 37C20 37C10 Secondary 37J10 

Notes

Acknowledgments

MB was partially supported by National Funds through FCT (Fundação para a Ciência e a Tecnologia) Project PEst-OE/MAT/UI0212/2011. CF was supported by FCT - Fundação para a Ciência e a Tecnologia SFRH/BD/33100/2007. JR was partially supported by FCT - Fundação para a Ciência e a Tecnologia through the project CMUP: PTDC/MAT/099493/2008. PV was partially supported by a CNPq-Brazil postdoctoral fellowship at University of Porto.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade da Beira InteriorCovilhãPortugal
  2. 2.Departamento de MatemáticaUniversidade do PortoPortoPortugal
  3. 3.Departamento de MatemáticaUniversidade Federal da BahiaSalvadorBrazil
  4. 4.CMUPUniversity of PortoPortoPortugal

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