By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics signify essentially the most very important contributions to our knowing of the complicated stability among reliable and risky motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the life of detailed 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 position in opting for the worldwide dynamics of the procedure. This publication presents a complete advent 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 history from which Mather’s concept was once 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 could be considered as a normal counterpart of KAM idea. He achieves this by way of guiding readers via a close illustrative instance, which additionally offers the foundation for introducing the most principles and ideas of the final idea. Sorrentino then describes the complete thought and its next advancements and purposes of their complete generality.
Shedding new gentle on John Mather’s innovative principles, this publication is sure to turn into a foundational textual content within the smooth examine 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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Extra info for Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes)