Formal Equivalence Between Normal Forms of Reversible and Hamiltonian Dynamical Systems

TL;DR

This paper demonstrates the formal equivalence between reversible and Hamiltonian dynamical systems using normal form theory, highlighting a deep connection in their mathematical structures.

Contribution

It establishes a formal equivalence between reversible and Hamiltonian vector fields through the application of normal form theory.

Findings

Reversible and Hamiltonian systems are formally equivalent.

Normal form theory is effective in establishing this equivalence.

The results deepen understanding of the structural similarities in dynamical systems.

Abstract

We show the existence of formal equivalences between reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory.