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arXiv · 2509.04248

Hamiltonian Systems as an Example of Invariant Measure

Daniel Ferreira Lopes
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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 their respective flows as an example of this invariance.

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Daniel Ferreira Lopes. 2025-09-04. Hamiltonian Systems as an Example of Invariant Measure. https://arxiv.org/abs/2509.04248

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