By Alfonso Sorrentino
John Mather's seminal works in Hamiltonian dynamics signify the most very important contributions to our figuring out of the complicated stability among sturdy and risky motions in classical mechanics. His novel approach—known as Aubry-Mather theory—singles out the life of detailed orbits and invariant measures of the method, which own a truly wealthy dynamical and geometric constitution. specifically, the linked invariant units play a number one position in settling on the worldwide dynamics of the method. This ebook offers a accomplished advent to Mather’s conception, and will function an interdisciplinary bridge for researchers and scholars from varied fields trying to acquaint themselves with the topic.
Starting with the mathematical historical past from which Mather’s conception 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 should be seen as a average counterpart of KAM concept. He achieves this through guiding readers via a close illustrative instance, which additionally offers the foundation for introducing the most principles and ideas of the overall conception. Sorrentino then describes the entire concept and its next advancements and purposes 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 smooth research of Hamiltonian systems.
Read or Download Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory: An Introduction to Aubry-Mather Theory (Mathematical Notes) PDF
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Extra resources 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