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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Action-Minimizing Methods in Hamiltonian Dynamics: An Introduction to Aubry-Mather Theory

Action-Minimizing Methods in Hamiltonian Dynamics: An Introduction to Aubry-Mather Theory

Sorrentino, Alfonso

Paperback

Series: Mathematical Notes, Book 50

General MathematicsPhysics

Currently unavailable to order

ISBN10: 0691164509
ISBN13: 9780691164502
Publisher: Princeton University Press
Published: May 26 2015
Pages: 128
Weight: 0.40
Height: 0.30 Width: 6.10 Depth: 9.20
Language: English

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical mechanics. His novel approach--known as Aubry-Mather theory--singles out the existence of special orbits and invariant measures of the system, which possess a very rich dynamical and geometric structure. In particular, the associated invariant sets play a leading role in determining the global dynamics of the system. This book provides a comprehensive introduction to Mather's theory, and can serve as an interdisciplinary bridge for researchers and students from different fields seeking to acquaint themselves with the topic.

Starting with the mathematical background from which Mather's theory was born, Alfonso Sorrentino first focuses on the core questions the theory aims to answer--notably the destiny of broken invariant KAM tori and the onset of chaos--and describes how it can be viewed as a natural counterpart of KAM theory. He achieves this by guiding readers through a detailed illustrative example, which also provides the basis for introducing the main ideas and concepts of the general theory. Sorrentino then describes the whole theory and its subsequent developments and applications in their full generality.

Shedding new light on John Mather's revolutionary ideas, this book is certain to become a foundational text in the modern study of Hamiltonian systems.

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