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Topological Dynamics and Topological Data Analysis

IWCTA 2018, Kochi, India, December 9–11

  • Conference proceedings
  • © 2021

Overview

Editors:
  1. Robert L. Devaney

    1. Department of Mathematics, Boston University, Boston, USA

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  2. Kit C. Chan

    1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, USA

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  3. P.B. Vinod Kumar

    1. Department of Mathematics, Rajagiri School of Engineering and Technology, Cochin, India

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  • Collects papers on topological dynamical systems and topological data analysis
  • Discusses topics on general topology, algebraic topology, differential topology, fuzzy topology, topological groups, and dynamics of operators network topology
  • Presents contributions from eminent international researchers

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 350)

Included in the following conference series:

Conference proceedings info: IWCTA 2018.

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Table of contents (23 papers)

  1. Front Matter

    Pages i-viii
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  2. An Overview of Unimodal Inverse Limit Spaces

    • H. Bruin
    Pages 1-13

  3. Dimension Theory of Some Non-Markovian Repellers Part I: A Gentle Introduction

    • Balázs Bárány, Michał Rams, Károly Simon
    Pages 15-48

  4. Dimension Theory of Some Non-Markovian Repellers Part II: Dynamically Defined Function Graphs

    • Balázs Bárány, Michał Rams, Károly Simon
    Pages 49-66

  5. Iterated Function Systems—A Topological Approach. Attractors

    • Krzysztof Leśniak
    Pages 67-74

  6. Zero-Dimensional Covers of Dynamical Systems

    • Hisao Kato
    Pages 75-84

  7. Chaotic Continua in Chaotic Dynamical Systems

    • Hisao Kato
    Pages 85-94

  8. Mandelpinski Necklaces in the Parameter Planes of Rational Maps

    • Robert L. Devaney, Sebastian M. Marotta
    Pages 95-119

  9. Some Examples of Hypercyclic Operators and Universal Sequences of Operators

    • Kit C. Chan
    Pages 121-126

  10. Some Basic Properties of Hypercyclic Operators

    • Kit C. Chan
    Pages 127-135

  11. The Testing Ground of Weighted Shift Operators for Hypercyclicity

    • Kit C. Chan
    Pages 137-145

  12. On \(\delta \)-deformations of Polygonal Dendrites

    • Dmitry Drozdov, Mary Samuel, Andrei Tetenov
    Pages 147-164

  13. General Position Theorem and Its Applications

    • Vladislav Aseev, Kirill Kamalutdinov, Andrei Tetenov
    Pages 165-176

  14. The nth Itarate of a Map with Dense Orbit

    • P. Amalraj, P. B. Vinod Kumar
    Pages 177-180

  15. Periodic Points of N-Dimensional Toral Automorphisms

    • K. Ali Akbar, T. Mubeena
    Pages 181-185

  16. Julia Sets in Topological Spaces

    • Sanil Jose, P. B. Vinod Kumar
    Pages 187-192

  17. Julia Set of Some Graphs Using Independence Polynomials

    • K. U. Sreeja, P. B. Vinod Kumar, P. B. Ramkumar
    Pages 193-202

  18. An Introduction to the Notion of Natural Pseudo-distance in Topological Data Analysis

    • Patrizio Frosini
    Pages 203-213

  19. A Brief Introduction to Multidimensional Persistent Betti Numbers

    • Andrea Cerri, Patrizio Frosini
    Pages 215-228

  20. Some New Methods to Build Group Equivariant Non-expansive Operators in TDA

    • Nicola Quercioli
    Pages 229-238
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  1. Topological Dynamics and Topological Data Analysis

Keywords

About this book

This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.

Editors and Affiliations

  • Department of Mathematics, Boston University, Boston, USA

    Robert L. Devaney

  • Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, USA

    Kit C. Chan

  • Department of Mathematics, Rajagiri School of Engineering and Technology, Cochin, India

    P.B. Vinod Kumar

About the editors

ROBERT L. DEVANEY is Professor at the Department of Mathematics, Boston University, USA. He received his Ph.D. from the University of California at Berkeley in 1973 under the direction of Prof. Stephen Smale. He is an author and the editor of 14 books including Fractals, Wavelets, and their Applications (Springer). He received the award for Distinguished University Teaching from the Northeastern Section of the Mathematical Association of America in 1994, the Boston University Scholar/Teacher of the Year Award in 1996 and the National Science Foundation Director's Award for Distinguished Teaching Scholars in 2002. His main area of research is dynamical systems, primarily complex analytic dynamics, including more general ideas about chaotic dynamical systems.


KIT C. CHAN is Professor and Chair of the Department of Mathematics and Statistics, Bowling Green State University, Ohio, USA. He earned his Ph.D. in mathematics from the University of Michigan in 1988. He is a member of the American Mathematical Society and the Mathematical Association of America. He has successfully guided six Ph.D. students and published over 33 papers in international journals of repute. His research areas are functional analysis and function theory.

VINOD KUMAR P. B. is Professor at the Department of Mathematics, Rajagiri School of Engineering & Technology, Cochin, Kerala, India. He is a member of American Mathematical Society, London Mathematical Society, Mathematical Association of America, Society for Industrial and Applied Mathematics, the Indian Mathematical Society and International Association of Engineers Council Member of Indian Mathematical Society. His research areas are chaos theory, fractal geometry, topology, dynamical systems, holomorphic dynamics and fractal image compression. 

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