IIT Jodhpur
Departmental Seminar by Divya Gupta on 27 November 2019

 27 November 2019, 5:00-5:30 PM, Room No.101, CSE Building

Title of Talk:
Topological Entropy
About the Speaker  
Divya Gupta  
Name of the supervisor  
Dr. V.V.M.S. Chandramouli  
One dimensional dynamical systems shows complicated dynamics and have the complex be- haviour. Topological entropy is a non-negative number which measures the complexity of the system. Topological entropy measures the exponential growth rate of the number of distinguish- able orbits as time increases. There are many ways to calculate the topological entropy, all of them have equal importance according to the system.  
Adler, Konheim and McAndrew [3] introduced the topological entropy for compact Hausdorff spaces. They assign a number to measure the size of any open cover of compact space. Bowen [4] defines entropy for uniformly continuous map on metric spaces. It uses the notion of epsilon- separated points. In this talk we discuss the definitions of topological entropy given by Adler and metric entropy given by Bowen with some examples. Then we discuss an algorithm to compute the topological entropy of interval map.
 1. Shannon, Claude Elwood. “A mathematical theory of communication.” Bell system technical journal 27.3 (1948): 379-423.
 2. Andrei N. Kolmogorov. “A new metric invariant of transient dynamical systems and automor- phisms in Lebesgue spaces.” Doklady Akademii Nauk SSSR (N.S.), 119 (1958), 861–864.
 3. Adler, Roy L., Alan G. Konheim, and M. Harry McAndrew.“Topological entropy.” Transactions of the American Mathematical Society 114.2 (1965): 309-319.
 4. Bowen, Rufus. ”Topological entropy for noncompact sets.“ Transactions of the American Math- ematical Society 184 (1973): 125-136.