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math.DS2024
Dynamics of globally minimizing orbits in contact Hamiltonian systems
Yang Xu, Jun Yan, Kai Zhao
In this paper, we study the asymptotic behavior of globally minimizing orbits of contact Hamiltonian systems. Under some assumptions, we prove that the -limit set of globally mi…
math.AP2024
Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations
Andrea Davini, Panrui Ni, Jun Yan +1
We study the asymptotic behavior of solutions of an equation of the form \begin{equation}\label{abs}\tag{*} G\big(x, D_x u,λu(x)\big) = c_0\qquad\hbox{in } \end{equation} on a c…
math.AP2024
Stability of solutions to contact Hamilton-Jacobi equation on the circle
Yang Xu, Jun Yan, Kai Zhao
Combing the weak KAM method for contact Hamiltonian systems and the theory of viscosity solutions for Hamilton-Jacobi equations, we study the Lyapunov stability and instability of…