"Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coord…
"Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coord…
The metric theory of Banach manifolds
by Akin, Ethan
fromLecture notes in mathematics (En ligne)
This book describes the category of metric manifolds and metric maps to which a broad class of theorems and constructions extend from the realm of compact manifolds. The category is a broad one because all paracompact manifolds admit metric structures.
"This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular success in the work of Perelm…
This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics. The work's first three chapters introduce the basic concepts of the theory, such as d…
