Topological Dynamics and Topological Data Analysis

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.

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.

Auteur

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.

Contenu

H. Bruin, An Overview of Unimodal Inverse Limit Spaces.- B. Barany, M. Rams, K. Simon, Dimension Theory of Some Non Markovian Rapellers Part I: A General Introduction.- B. Barany, M. Rams, K. Simon, Dimension Theory of Some Non Markovian Repellers: Part II: Dynamically Defined Function Graphs.- K. Lesniak, Iterated Function Systems - A Topological Approach Attractors.- H. Kato, Zero Dimensional Covers of Dynamical Systems.- H. Kato, Chaotic Continua in Chaotic Dynamical Systems.- R. L. Devaney, S. M. Marotta, Mandelpinski Necklaces in the Parameter Planes of Rational Maps.- Kit C Chan, Some Examples of Hypercyclic Operators and Universal Sequences of Operators.- Kit C Chan, Some Basic Properties of Hypercyclic Operators.- Kit C Chan, The Testing Ground of Weighted Shift Operators for Hypercyclicity.- D. Drozdov, M. Samuel, A. Tetenov, On -deformations of Polygonal Dendrites.- A. Tetenov, K. Kamalutdinov, V. Aseev, General Position Theorems and its Applications.- A. Raj P, V. Kumar P B, The nth iterate of a map with dense orbit.- Aswathy R K, S. Mathew, Finite Products of Irregular Iterated Function Systems and Their Separation Properties.- A. Akbar, Mubeena T, Periodic Points of N-dimensional Toral Automorphisms.- S. Jose, V. Kumar P B, Julia Sets in Topological Spaces.- K U Sreeja, V. Kumar P B, Ramkumar P B, Julia, Sets of Some Graphs Using Independence Polynomials.- P. Frosini, An Introduction to the Notion of Natural Pseudo Distance in Topological Data Analysis.- A. Cerri, P. Frosini, A Brief Introduction to Multidimensional Persistent Betti Numbers.- N. Quercioli, Some New Methods to Build Group Equivariant Non Expansive Operators in TDA.- Y. Dabaghian, Topological Stability of the Hippocampal Spatial Map and Synaptic Transience.- A. Jacob, Ramkumar P B, Intuitionistic Fuzzy Graph Morphological Topology.- A. G. Pillai, Ramkumar P B, Some Properties of the Bitopological Space Associated with the 3-Uniform Semigraph of Cycle graph.- D. Chandran R, Ramkumar P B, Hypergraph Topology.