Variational Modelling: Energies, gradient flows, and large deviations
by Mark A. Peletier
Publisher: arXiv 2014
Number of pages: 64
The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the methodology itself in great detail, and explain why this is a rational modelling route.
Home page url
Download or read it online here:
by Alexey Shabat, Elena Kartashova - arXiv
A preliminary version of the textbook on integrable systems. Contents: General notions and ideas; Riccati equation; Factorization of linear operators; Commutativity of linear operators; Integrability of non-linear PDEs; Burgers-type equations.
by Evans M. Harrell II
Class notes for an introductory course on dynamical systems and chaos for mathematicians, physicists, and engineers. The text concentrates on models rather than proofs in order to bring out the concepts of dynamics and chaos.
by P. Rabier - Tata Institute of Fundamental Research
This set of lectures gives a synthetic exposition for the study of one-parameter bifurcation problems. By this, we mean the analysis of the structure of their set of solutions through the same type of general arguments in various situations.
by Thomas Ward - University of East Anglia
These notes cover a very short introduction to measure-theoretic and topological entropy, and are aimed at understanding part of Yuzvinskii's formula for the entropy of compact group automorphisms. Based on a course at the Ohio State University.