Hyperbolicity and Stability for Hamiltonian flows
M. Bessa, M. J. Torres, J. Rocha
TL;DR
This paper proves that Hamiltonian star systems on symplectic manifolds are Anosov, confirming the stability conjecture for Hamiltonians and extending previous 4-dimensional results to higher dimensions.
Contribution
It establishes that Hamiltonian star systems are Anosov, providing a significant generalization of stability results to higher-dimensional symplectic manifolds.
Findings
Hamiltonian star systems are Anosov.
Proof of the stability conjecture for Hamiltonians.
Extension of 4D results to higher dimensions.
Abstract
We prove that a Hamiltonian star system, defined on a 2d-dimensional symplectic manifold M, is Anosov. As a consequence we obtain the proof of the stability conjecture for Hamiltonians. This generalizes the 4-dimensional results in [6].
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Geometry and complex manifolds