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arXiv · 2009.12532

Variational attraction of the KAM torus for the conformally symplectic system

Liang Jin·Jianlu Zhang·Kai Zhao
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Abstract

For the conformally symplectic system \[ \left\{ \begin{aligned} \dot{q}&=H_p(q,p),\quad(q,p)\in T^*\mathbb{T}^n\\ \dot p&=-H_q(q,p)-\lambda p, \quad \lambda>0 \end{aligned} \right. \] with a positive definite Hamiltonian, we discuss the variational significance of invariant Lagrangian graphs and explain how the KAM torus impacts the $W^{1,\infty}-$convergence speed of the Lax-Oleinik semigroup.

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Liang Jin, Jianlu Zhang, Kai Zhao. 2020-09-26. Variational attraction of the KAM torus for the conformally symplectic system. https://arxiv.org/abs/2009.12532

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