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math.DS2007
On the Hausdorff Dimension of the Mather Quotient
Albert Fathi, Alessio Figalli, Ludovic Rifford
Under appropriate assumptions on the dimension of the ambient manifold and the regularity of the Hamiltonian, we show that the Mather quotient is small in term of Hausdorff dimensi…
math.DS2007
Invariant measures of Hamiltonian systems with prescribed asymptotic Maslov index
Alberto Abbondandolo, Alessio Figalli
We study the properties of the asymptotic Maslov index of invariant measures for time-periodic Hamiltonian systems on the cotangent bundle of a compact manifold M. We show that if…
math.DS2006
High action orbits for Tonelli Lagrangians and superlinear Hamiltonians on compact configuration spaces
Alberto Abbondandolo, Alessio Figalli
Multiplicity results for solutions of various boundary value problems are known for dynamical systems on compact configuration manifolds, given by Lagrangians or Hamiltonians which…