By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics symbolize one of the most very important contributions to our realizing of the advanced stability among sturdy and volatile motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the lifestyles of particular orbits and invariant measures of the process, which own a truly wealthy dynamical and geometric constitution. specifically, the linked invariant units play a number one function in settling on the worldwide dynamics of the method. This e-book offers a entire creation to Mather’s concept, and will function an interdisciplinary bridge for researchers and scholars from diverse fields looking to acquaint themselves with the topic.
Starting with the mathematical heritage from which Mather’s concept used to be born, Alfonso Sorrentino first specializes in the center questions the idea goals to answer—notably the future of damaged invariant KAM tori and the onset of chaos—and describes the way it might be considered as a common counterpart of KAM idea. He achieves this by way of guiding readers via an in depth illustrative instance, which additionally offers the foundation for introducing the most principles and ideas of the final conception. Sorrentino then describes the entire idea and its next advancements and purposes of their complete generality.
Shedding new mild on John Mather’s progressive principles, this publication is sure to develop into a foundational textual content within the sleek learn of Hamiltonian systems.
Read or Download Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes) PDF
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Additional info for Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes)
Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes) by Alfonso Sorrentino