Open AccessA stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II
Author(s) -
В. А. Калошин,
Brian R. Hunt
Publication year - 2001
Publication title -
electronic research announcements of the american mathematical society
Language(s) - English
Resource type - Journals
ISSN - 1079-6762
DOI - 10.1090/s1079-6762-01-00091-9
Subject(s) - algorithm , annotation , semantics (computer science) , mathematics , type (biology) , computer science , artificial intelligence , programming language , ecology , biology
We continue the previous article’s discussion of bounds, for prevalent diffeomorphisms of smooth compact manifolds, on the growth of the number of periodic points and the decay of their hyperbolicity as a function of their period n n . In that article we reduced the main results to a problem, for certain families of diffeomorphisms, of bounding the measure of parameter values for which the diffeomorphism has (for a given period n n ) an almost periodic point that is almost nonhyperbolic. We also formulated our results for 1 1 -dimensional endomorphisms on a compact interval. In this article we describe some of the main techniques involved and outline the rest of the proof. To simplify notation, we concentrate primarily on the 1 1 -dimensional case.