Hamiltonian Systems as an Example of Invariant Measure
Daniel Ferreira Lopes
Published: 2025/9/4
Abstract
Hamiltonian systems are a classical example in the ergodic theory of flows with an invariant measure. In this matter, we present a brief introduction to measure theory and prove the Poincare recurrence theorem to present the conditions for a system to be conservative. In the following, we discuss the Hamiltonian differential equations, vector fields, and its respective flows as an example of this invariance.