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Differential Equations and Dynamical Systems

2 USUZCAMP, Urgench, Uzbekistan, August 8–12, 2017

  • Conference proceedings
  • © 2018

Overview

Editors:
  1. Abdulla Azamov

    1. Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

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  2. Leonid Bunimovich

    1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

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  3. Akhtam Dzhalilov

    1. Turin Polytechnic University, Tashkent, Uzbekistan

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  4. Hong-Kun Zhang

    1. Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, USA

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  • 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

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 268)

Included in the following conference series:

Conference proceedings info: USUZCAMP 2017.

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About this book

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.

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Keywords

Table of contents (14 papers)

  1. Front Matter

    Pages i-vi
    Download chapter PDF

  2. On Linearization of Circle Diffeomorphisms

    • Akhadkulov Habibulla, Dzhalilov Akhtam, Konstantin Khanin
    Pages 1-8

  3. The Fujita and Secondary Type Critical Exponents in Nonlinear Parabolic Equations and Systems

    • Aripov Mersaid
    Pages 9-23

  4. A Language of Terms of Taylor’s Formula for Quadratic Dynamical Systems and Its Fractality

    • Abdulla Azamov
    Pages 25-40

  5. Discrete-Numerical Tracking Method for Constructing a Poincaré Map

    • Abdulla Azamov, Akhmedov Odiljon, Tilavov Asliddin
    Pages 41-53

  6. A Discrete Mathematical Model for Heat Transfer Process in Rotating Regenerative Air Preheater

    • Bekimov Mansur, Fathalla A. Rihan
    Pages 55-61

  7. On Attractors of Isospectral Compressions of Networks

    • Leonid Bunimovich, Longmei Shu
    Pages 63-73

  8. On Herman’s Theorem for Piecewise Smooth Circle Maps with Two Breaks

    • Akhtam Dzhalilov, Alisher Jalilov, Dieter Mayer
    Pages 75-100

  9. Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

    • Ibragimov Gafurjan, Usman Waziri, Idham Arif Alias, Zarina Bibi Ibrahim
    Pages 101-113

  10. Invariance Principles for Ergodic Systems with Slowly \(\alpha \)-Mixing Inducing Base

    • Jianyu Chen, Kien Nguyen
    Pages 115-126

  11. Central Limit Theorem for Billiards with Flat Points

    • Kien Nguyen, Hong-Kun Zhang
    Pages 127-140

  12. Almost Sure Rates of Mixing for Random Intermittent Maps

    • Marks Ruziboev
    Pages 141-152

  13. Conjugations Between Two Critical Circle Maps With Non-integer Exponents

    • Utkir Safarov
    Pages 153-168

  14. \(\varepsilon \)-Positional Strategy in the Second Method of Differential Games of Pursuit

    • Tukhtasinov Muminjon
    Pages 169-182

  15. Unilateral Ball Potentials on Generalized Lebesgue Spaces with Variable Exponent

    • Yakhshiboev Makhmadiyor
    Pages 183-195
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Other volumes

  1. Algebra, Complex Analysis, and Pluripotential Theory

  2. Differential Equations and Dynamical Systems

Editors and Affiliations

  • Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

    Abdulla Azamov

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Leonid Bunimovich

  • Turin Polytechnic University, Tashkent, Uzbekistan

    Akhtam Dzhalilov

  • Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, USA

    Hong-Kun Zhang

Bibliographic Information

  • Book Title: Differential Equations and Dynamical Systems

  • Book Subtitle: 2 USUZCAMP, Urgench, Uzbekistan, August 8–12, 2017

  • Editors: Abdulla Azamov, Leonid Bunimovich, Akhtam Dzhalilov, Hong-Kun Zhang

  • Series Title: Springer Proceedings in Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-3-030-01476-6

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2018

  • Hardcover ISBN: 978-3-030-01475-9Published: 21 October 2018

  • Softcover ISBN: 978-3-030-13180-7Published: 10 December 2019

  • eBook ISBN: 978-3-030-01476-6Published: 20 October 2018

  • Series ISSN: 2194-1009

  • Series E-ISSN: 2194-1017

  • Edition Number: 1

  • Number of Pages: VI, 195

  • Number of Illustrations: 12 b/w illustrations, 17 illustrations in colour

  • Topics: Dynamical Systems and Ergodic Theory, Partial Differential Equations

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