Differential Equations and Dynamical Systems

1. Front Matter

   Pages i-vi

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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

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.

• Partial Differential Equations
• Finite Dynamics
• Mathematic Billiards
• Random Dynamics
• Dynamical Systems of Biology
• Dynamical Systems of Medicine
• Quadratic Systems
• No-slip Billiards
• Expanding Maps
• Renormalizations
• Chaos
• Circole Homeomorphisms
• Invariant Measures
• Rigidity Problem
• Congugacies
• Lodka-Volterra Operators
• Random Intermittent Maps
• Projective Plane
• Pursuit Game

• 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

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