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Tonelli Lagrangians and Hamiltonians on Compact Manifolds

Tonelli Lagrangians and Hamiltonians on Compact Manifolds

Chapter:
(p.1) Chapter One Tonelli Lagrangians and Hamiltonians on Compact Manifolds
Source:
Action-minimizing Methods in Hamiltonian Dynamics (MN-50)
Author(s):
Alfonso Sorrentino
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164502.003.0001

This chapter introduces the basic setting: Tonelli Lagrangians and Hamiltonians on a compact manifold. It discusses their main properties and some examples, and provides the opportunity to recall some basic facts on Lagrangian and Hamiltonian dynamics (and on their mutual relation), which will be of fundamental importance in the discussion thereafter.

Keywords:   Tonelli Lagrangians, Hamiltonians, compact manifold, Lagrangian dynamics, Hamiltonian dynamics

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