Lecture notes on Mather's theory for Lagrangian systems
Alfonso Sorrentino
TL;DR
This paper provides an accessible introduction to Mather's theory, focusing on Tonelli Lagrangian and Hamiltonian systems, based on lecture notes from multiple academic courses.
Contribution
It offers a comprehensive, beginner-friendly overview of Mather's theory tailored for students and researchers new to the topic.
Findings
Clarifies key concepts of Mather's theory
Summarizes main results and applications
Provides educational insights into Lagrangian systems
Abstract
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at University of Cambridge (academic year 2009-2010) and at Universitat Polit\`ecnica de Catalunya (June 2010).
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Taxonomy
TopicsQuantum chaos and dynamical systems · Numerical methods for differential equations · Nonlinear Waves and Solitons