By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics symbolize probably the most vital contributions to our figuring out of the complicated stability among solid and volatile motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the lifestyles of specified 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 selecting the worldwide dynamics of the approach. This e-book offers a entire advent to Mather’s conception, and will function an interdisciplinary bridge for researchers and scholars from assorted fields trying to acquaint themselves with the topic.
Starting with the mathematical heritage from which Mather’s conception 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 will be seen as a normal counterpart of KAM conception. He achieves this through guiding readers via a close illustrative instance, which additionally offers the root for introducing the most principles and ideas of the final idea. Sorrentino then describes the full conception and its next advancements and functions of their complete generality.
Shedding new mild on John Mather’s progressive principles, this ebook is sure to develop into a foundational textual content within the sleek 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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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