# Invariant Lagrange submanifolds of dissipative systems

## TL;DR

This paper investigates invariant Lagrange submanifolds within dissipative systems by analyzing solutions to modified Hamilton-Jacobi equations on compact manifolds.

## Contribution

It introduces a novel approach to understanding invariant structures in dissipative systems through modified Hamilton-Jacobi equations.

## Key findings

- Identification of conditions for invariance of Lagrange submanifolds
- Existence results for solutions to the modified Hamilton-Jacobi equations
- Insights into the stability properties of these solutions

## Abstract

We study solutions of modified Hamilton-Jacobi equations H(du/dq,q) + cu(q) = 0, q \in M, on a compact manifold M .