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- W2037534459 abstract "We prove that all the Tonelli Hamiltonians defined on the cotangent bundle $T^*T^n$ of the $n$-dimensional torus that have no conjugate points are $C^0$ integrable, i.e. $T^*T^n$ is $C^0$ foliated by a family $Fc$ of invariant $C^0$ Lagrangian graphs. Assuming that the Hamiltonian is $C^infty$, we prove that there exists a $G_delta$ subset $Gc$ of $Fc$ such that the dynamics restricted to every element of $Gc$ is strictly ergodic. Moreover, we prove that the Lyapunov exponents of every $C^0$ integrable Tonelli Hamiltonian are zero and deduce that the metric and topological entropies vanish." @default.
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- W2037534459 date "2013-09-24" @default.
- W2037534459 modified "2023-10-18" @default.
- W2037534459 title "Tonelli Hamiltonians without conjugate points and $C^0$ integrability" @default.
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