Differential Equations and Dynamical Systems

This book features papers presented during a special session on dynamical systems, mathematical physics, and partial differential equations. Research articles are devoted to broad complex systems and models such as qualitative theory of dynamical systems, theory of games, circle diffeomorphisms, piecewise smooth circle maps, nonlinear parabolic systems, quadtratic dynamical systems, billiards, and intermittent maps. Focusing on a variety of topics from dynamical properties to stochastic properties of dynamical systems, this volume includes discussion on discrete-numerical tracking, conjugation between two critical circle maps, invariance principles, and the central limit theorem. Applications to game theory and networks are also included. Graduate students and researchers interested in complex systems, differential equations, dynamical systems, functional analysis, and mathematical physics will find this book useful for their studies. The special session was part of the second USA-Uzbekistan Conference on Analysis and Mathematical Physics held on August 8-12, 2017 at Urgench State University (Uzbekistan). The conference encouraged communication and future collaboration among U.S. mathematicians and their counterparts in Uzbekistan and other countries. Main themes included algebra and functional analysis, dynamical systems, mathematical physics and partial differential equations, probability theory and mathematical statistics, and pluripotential theory. A number of significant, recently established results were disseminated at the conference's scheduled plenary talks, while invited talks presented a broad spectrum of findings in several sessions. Based on a different session from the conference, Algebra, Complex Analysis, and Pluripotential Theory is also published in the Springer Proceedings in Mathematics & Statistics Series.

Increases significantly readers' understanding of the statistical properties of dynamical systems of physical origin Covers topics that are central to equilibrium and non-equilibrium physical systems Uses methodologies that are of great interest to researchers in chemistry, big data analysis, and finance Discusses correlations of time series driven by dynamical systems to help readers understand situations leading to failures and therefore to reduce risks in the future

Inhalt
Habibulla, A., Akhtam, D. and Khanin, K: On Linearization of Circle Diffeomorphisms.- Mersaid, A: The Fujita and Secondary Type Critical Exponents in Nonlinear Parabolic Equations and Systems.- Abdulla, A: A Language of Terms of Taylor's Formula for Quadratic Dynamical Systems and its Fractality.- Abdulla, A., Odiljon, A. and Asliddin, T: Discrete-Numerical Tracking Method for Constructing a Poincare Map.- Mansur, B. and Rihan, F. A: A Discrete Mathematical Model for Heat Transfer Process in Rotating Regenerative Air Preheater.- Leonid, B. and Shu, L: On Attractors of Isospectral Compressions of Networks.- Akhtam, D., Alisher, J. and Dieter, M: On Herman's Theorem for Piecewise Smooth Circle Maps With Two Breaks.- Gafurjan, I., Waziri, U., Alias, I. A. and Ibrahim, Z. B: Pursuit Game for an Innite System of First-Order Differential Equations with Negative Coefcients.- Chen, J. and Nguyen, K: Invariance Principles for Ergodic Systems with Slowly -mixing Inducing Base.- Nguyen, K. and Zhang, H-K: Central Limit Theorem for Billiards With Flat Points.- Marks, R: Almost Sure Rates of Mixing for Random Intermittent Maps.- Utkir, S: Conjugations Between Wwo Critical Circle Maps With Non-Integer Exponents.- Muminjon, T: -Positional Strategy in the Second Method of Differential Games of Pursuit.- Makhmadiyor, Y: Unilateral Ball Potentials on Generalized Lebesgue Spaces With Variable Exponent.