# 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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