Porfirio Toledo, " Weak KAM Solutions of a Discrete-Time Hamilton-Jacobi Equation in a Minimax Framework ", Discrete Dynamics in Nature and Society, vol. , Article ID , 12 pages, https: instead of a Lagrangian, Theorem 1 is analogue to Weak KAM Theorem. Read more about Weak KAM Theorem: Lagrangian Dynamics and viscosity solutions of PDEs; Topics in High-Dimensional Statistics. Read more about Topics in High-Dimensional Statistics; College Algebra. Study of the properties of algebraic, exponential, and logarithmic functions as . A key feature of the book is the early introduction of geometric (differential manifold) ideas, as well as detailed treatment of topics in nonlinear dynamics (such as the KAM theorem) and continuum dynamics (including solitons). The book contains many worked examples and . Weak KAM theory for nonregular commuting Hamiltonians. Discrete & Continuous Dynamical Systems - B, , 18 (1): doi: /dcdsb [6] Katarzyna Grabowska. Lagrangian and Hamiltonian formalism in Field Theory: A simple model.

In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an ally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newton’s gravity) divided by the distance. Books. Publishing Support. Login. Login. Forgotten password? Create account. Benefits of a My IOPscience account. The book concludes with an appendix discussing the relevance of the KAM theorem to the ergodic hypothesis and the second law of thermodynamics. Lectures on Nonlinear Mechanics and Chaos Theory is written in the easy conversational style of a great teacher. -Lagrangian and Hamiltonian dynamics-Hamilton-Jacobi equation and dynamics-Viscosity solutions of Hamilton-Jacobi equation and dynamics-Aubry and Mather sets. Minimizing measures; Time permitting we will give some applications of the methods: discrete weak KAM theory.-Lyapunov functions in dynamics-time functions in Lorentz spaces.

Here, we extend the weak KAM and Aubry-Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton-Jacobi equations, and the long-time behavior of time-dependent systems. Classical dynamics of continuous systems, waves on a string and membranes. Noether theorem for continuous systems ; The canonical stress tensor ; Chaotic and non-linear dynamics. Poincare maps KAM theorem The goal of this course is for you (the student) to be able to solve physics problems associated with these topics. Buy Classical Dynamics: A Contemporary Approach 98 edition () by NA for up to 90% off at Weak KAM theory. Aubry-Mather theory. Other topics to be discussed if there is time or to be assigned as projects. The following are more tentative: Ergodic theory. The origins of ergodic theory and the ergodic hypothesis. Koopman formalism. Von Neuman Ergodic theorem. Birkho Ergodic theorem. Mixing Entropy and Shannon Mc Millan Breiman theorem.