Small perturbations of a contact Hamilton-Jacobi equation preserve the existence and stability of viscosity solutions near a Lyapunov stable solution.
Dynamics of globally minimizing orbits in contact Hamiltonian systems
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In this paper, we study the asymptotic behavior of globally minimizing orbits of contact Hamiltonian systems. Under some assumptions, we prove that the $\omega$-limit set of globally minimizing orbits is contained in the set of semi-static orbits.
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The existence and stability of viscosity solutions to perturbed contact Hamilton-Jacobi equations
Small perturbations of a contact Hamilton-Jacobi equation preserve the existence and stability of viscosity solutions near a Lyapunov stable solution.