Differential Equations

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

By Alfonso Sorrentino

John Mather's seminal works in Hamiltonian dynamics signify probably the most very important contributions to our knowing of the advanced stability among sturdy and volatile motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the lifestyles of detailed orbits and invariant measures of the approach, which own a really wealthy dynamical and geometric constitution. specifically, the linked invariant units play a number one function in making a choice on the worldwide dynamics of the procedure. This booklet offers a entire advent to Mather’s concept, and will function an interdisciplinary bridge for researchers and scholars from diverse fields trying to acquaint themselves with the topic.

Starting with the mathematical history from which Mather’s thought used to be born, Alfonso Sorrentino first makes a speciality of the middle 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 typical counterpart of KAM concept. He achieves this by way of guiding readers via a close illustrative instance, which additionally presents the root for introducing the most rules and ideas of the final idea. Sorrentino then describes the full thought and its next advancements and purposes of their complete generality.

Shedding new mild on John Mather’s progressive principles, this e-book is sure to develop into a foundational textual content within the sleek examine of Hamiltonian systems.

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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


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