By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics symbolize the most vital contributions to our realizing of the complicated stability among solid and volatile motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the life of precise 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 identifying the worldwide dynamics of the procedure. This booklet offers a accomplished advent to Mather’s concept, and will function an interdisciplinary bridge for researchers and scholars from diverse fields looking to acquaint themselves with the topic.
Starting with the mathematical historical past from which Mather’s conception was once born, Alfonso Sorrentino first makes a speciality of 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 will be seen as a usual counterpart of KAM conception. He achieves this via guiding readers via an in depth illustrative instance, which additionally offers the foundation for introducing the most principles and ideas of the final concept. Sorrentino then describes the full idea and its next advancements and functions of their complete generality.
Shedding new gentle on John Mather’s progressive rules, this publication is bound to turn into a foundational textual content within the sleek research of Hamiltonian systems.
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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