Action-minimizing Methods in Hamiltonian Dynamics (MN-50): by Alfonso Sorrentino

By Alfonso Sorrentino

John Mather's seminal works in Hamiltonian dynamics characterize one of the most very important contributions to our knowing of the advanced stability among strong and volatile motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the life of targeted orbits and invariant measures of the process, which own a truly wealthy dynamical and geometric constitution. particularly, the linked invariant units play a number one position in selecting the worldwide dynamics of the approach. This ebook presents a entire advent to Mather’s concept, and will function an interdisciplinary bridge for researchers and scholars from various fields trying to acquaint themselves with the topic.

Starting with the mathematical historical past from which Mather’s idea was once born, Alfonso Sorrentino first specializes in the middle questions the speculation 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 ordinary 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 principles and ideas of the final conception. Sorrentino then describes the entire idea and its next advancements and functions of their complete generality.

Shedding new mild on John Mather’s innovative principles, this ebook is bound to develop into a foundational textual content within the glossy learn of Hamiltonian systems.

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