Generating Forms for Exact Volume-Preserving Maps

TL;DR

This paper develops a general theory of implicit generating forms for volume-preserving diffeomorphisms, extending classical generating function formulas from symplectic twist maps to a broader setting.

Contribution

It introduces a unified framework for generating forms of volume-preserving maps, generalizing classical symplectic formulas.

Findings

Established a theory of implicit generating forms

Generalized classical formulas for symplectic twist maps

Provides tools for analyzing volume-preserving diffeomorphisms

Abstract

We study the group of volume-preserving diffeomorphisms on a manifold. We develop a general theory of implicit generating forms. Our results generalize the classical formulas for generating functions of symplectic twist maps.