By Alfonso Sorrentino

John Mather's seminal works in Hamiltonian dynamics symbolize probably 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 precise orbits and invariant measures of the procedure, which own a really wealthy dynamical and geometric constitution. particularly, the linked invariant units play a number one function in making a choice on the worldwide dynamics of the process. This e-book offers a finished creation to Mather's concept, and will function an interdisciplinary bridge for researchers and scholars from diversified fields trying to acquaint themselves with the topic.

Starting with the mathematical history from which Mather's idea used to be born, Alfonso Sorrentino first makes a speciality of the center questions the speculation 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 average counterpart of KAM conception. He achieves this through guiding readers via an in depth illustrative instance, which additionally offers the root for introducing the most rules and ideas of the overall concept. Sorrentino then describes the full concept and its next advancements and purposes of their complete generality.

Shedding new mild on John Mather's progressive principles, this booklet is bound to develop into a foundational textual content within the smooth research of Hamiltonian systems.

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