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math.DS2021
Lipschitz sub-actions for locally maximal hyperbolic sets of a maps
Xifeng Su, Philippe Thieullen, Wenzhe Yu
Livšic theorem asserts that, for Anosov diffeomorphisms/flows, a Lipschitz observable is a coboundary if all its Birkhoff sums on every periodic orbits are equal to zero. The trans…
math.DS2021
Essential forward weak KAM solution for the convex Hamilton-Jacobi equation
Xifeng Su, Jianlu Zhang
For a convex, coercive continuous Hamiltonian on a compact closed Riemannian manifold , we construct a unique forward weak KAM solution of \[ H(x, d_x u)=c(H) \] by a vanishing…