By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics characterize essentially the most vital contributions to our knowing of the complicated stability among solid and risky motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the lifestyles of unique 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 function in selecting the worldwide dynamics of the approach. This publication presents a complete advent to Mather’s conception, and will function an interdisciplinary bridge for researchers and scholars from diversified 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 idea goals to answer—notably the future of damaged invariant KAM tori and the onset of chaos—and describes the way it should be seen as a usual counterpart of KAM conception. He achieves this via guiding readers via a close illustrative instance, which additionally presents the root for introducing the most principles and ideas of the final conception. 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 e-book is bound to turn into a foundational textual content within the glossy learn 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