Herglotz’ Generalized Variational Principle and Contact Type Hamilton-Jacobi Equations |
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Arguably, the two most popular accelerated or momentum-based optimization methods are
Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different …

In this paper, we focus on action-minimizing methods for contact Hamiltonian systems.
Based on implicit variational principles introduced in Wang et al.(Nonlinearity 30: 492–515 …

We develop an elementary method to give a Lipschitz estimate for the minimizers in the
problem of Herglotz'variational principle proposed in the paper (P. Cannarsa, W. Cheng, K …

This article is devoted to studying the vanishing contact structure problem which is a
generalization of the vanishing discount problem. Let H λ (x, p, u) be a family of …

We extend to higher dimensions the notion of Birkhoff attractor of a dissipative map. We
prove that this notion coincides with the classical Birkhoff attractor defined by Birkhoff in …

We describe a method, based on contact topology, of showing the existence of semi-infinite
trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and …

For any compact connected manifold M, we consider the generalized contact Hamiltonian H
(x, p, u) defined on T∗ M× R which is convex in p and monotonically increasing in u. Let u ε …

Dynamics of globally minimizing orbits in contact Hamiltonian systems arXiv:2412.20658v1 [math.DS]
30 Dec 2024 Page 1 Dynamics of globally minimizing orbits in contact Hamiltonian systems …

We consider the evolutionary Hamilton-Jacobi equation\begin {align*} w_t (x, t)+ H (x, Dw (x,
t), w (x, t))= 0,\quad (x, t)\in M\times [0,+\infty),\end {align*} where $ M $ is a compact …