首页|Aubry-Mather theory for contact Hamiltonian systems Ⅲ
Aubry-Mather theory for contact Hamiltonian systems Ⅲ
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By exploiting the contact Hamiltonian dynamics(T*M × R,Φt)around the Aubry set of contact Hamiltonian systems,we provide a relation among the Mather set,the Φt-recurrent set,the strongly static set,the Aubry set,the Mané set,and the Φt-non-wandering set.Moreover,we consider the strongly static set,as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing case.We show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser(KAM)solutions and the existence of transitive orbits around the Aubry set.
Aubry-Mather theoryweak KAM theorycontact Hamiltonian systemsHamilton-Jacobi equations
Panrui Ni、Lin Wang
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Shanghai Center for Mathematical Sciences,Fudan University,Shanghai 200433,China
School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China
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