Special Session 94: Dynamics and Variational Methods of Quasi-Hamiltonian Systems

Periodic, Quasi-Periodic and Almost Periodic Solutions of the Hamilton-Jacobi Equation
Kai Zhao
Tongji university
Peoples Rep of China
Co-Author(s):    Kai Zhao
Abstract:
It is well known that there exist no non-trivial periodic solutions for classical Hamilton-Jacobi equations. Combining the weak KAM method for contact Hamiltonian systems with the viscosity solution theory of the Hamilton-Jacobi equation, we have recently investigated the problem of time periodic solutions for contact Hamilton-Jacobi equations. Under certain conditions, quasi-periodic solutions and almost periodic solutions can also emerge. Furthermore, we have explored the chaotic nature of the large time behavior of the solutions.