Calculating Topological Entropy

Details Calculating Topological Entropy Calculating Topological Entropy

Dec 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jsp....89.1017b&link_type=abstract

Journal of Statistical Physics, Volume 89, Issue 5-6, pp. 1017-1033

Mathematics

Logic

1

Topological Entropy, Algorithm, Power Method, Markov Map

Scientific paper

The attempt to find effective algorithms for calculating the topological entropy of piecewise monotone maps of the interval having more than three monotone pieces has proved to be a difficult problem. The algorithm introduced here is motivated by the fact that if f: [0, 1] → [0, 1] is a piecewise monotone map of the unit interval into itself, then h( f)=limn→∞ (1/ n) log Var( f n), where h( f) is the topological entropy of f, and Var( f n) is the total variation of f n. We show that it is not feasible to use this formula directly to calculate numerically the topological entropy of a piecewise monotone function, because of the slow convergence. However, a close examination of the reasons for this failure leads ultimately to the modified algorithm which is presented in this paper. We prove that this algorithm is equivalent to the standard power method for finding eigenvalues of matrices (with shift of origin) in those cases for which the function is Markov, and present encouraging experimental evidence for the usefulness of the algorithm in general by applying it to several one-parameter families of test functions.

Affiliated with

Also associated with

No associations

Rating

Calculating Topological Entropy does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Calculating Topological Entropy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Calculating Topological Entropy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-1662348