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摘要
En 中文
Given a Tonelli Hamiltonian H:T*M of class C-k, with k4, we prove the following results: (1) Assume there is a critical viscosity subsolution that is of class Ck+1 in an open neighborhood of a positive orbit of a recurrent point of the projected Aubry set. Then there exists a potential V : M of class Ck-1, small in the C-2 topology, for which the Aubry set of the new Hamiltonian H+V is either an equilibrium point or a periodic orbit. (2) For every >0 there exists a potential V : M of class Ck-2, with VC1, for which the Aubry set of the new Hamiltonian H+V is either an equilibrium point or a periodic orbit. The latter result solves in the affirmative the Mane density conjecture in the C-1 topology. (c) 2015 Wiley Periodicals, Inc.
Keyword:
HAMILTON-JACOBI EQUATIONS
VISCOSITY SOLUTIONS
COMPACT MANIFOLDS
EXISTENCE
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IF:
2.7
论文数:
1.5K
被引数:
1.1W
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