By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics signify probably the most vital contributions to our knowing of the advanced stability among sturdy 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 really wealthy dynamical and geometric constitution. specifically, the linked invariant units play a number one position in selecting the worldwide dynamics of the method. This publication offers a accomplished advent to Mather’s conception, and will function an interdisciplinary bridge for researchers and scholars from varied 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 makes a speciality of 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 will be considered as a traditional counterpart of KAM conception. He achieves this by way of guiding readers via a close illustrative instance, which additionally presents the foundation for introducing the most rules and ideas of the overall concept. Sorrentino then describes the complete conception and its next advancements and purposes of their complete generality.
Shedding new gentle on John Mather’s progressive rules, this booklet 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