The Geometry Of Higher-Order Hamilton Spaces; Applications to Hamiltonian Mechanics

TL;DR

This work explores the geometric structures of higher-order Hamilton spaces, focusing on their applications in Hamiltonian mechanics through Lagrange and dual manifold geometries, including Legendre transformations.

Contribution

It provides a comprehensive geometric framework for higher-order Hamilton spaces and their duals, integrating Lagrange geometry and Legendre transformations in a unified approach.

Findings

Develops the geometry of higher-order Hamilton spaces

Analyzes dual manifolds via Legendre transformation

Provides applications to Hamiltonian mechanics

Abstract

The book can be divided in three parts: the Lagrange geometry of order $k$, presented in the first three chapters, the geometrical theory of the dual manifolds $T^{*k}M$ - chapters 4-7 and the geometry of Hamilton spaces of order $k$ and their subspaces, contained in the last four chapters. They are studied directly and as 'dual' geometry, via Legendre transformation.