About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Commun. Math. Phys.
Paper
Self-similar constructions in smooth dynamics: Rigidity, smoothness and dimension
Abstract
In the first part of this paper, for each d≥2, we construct diffeomorphisms of the d-dimensional ball which have zero entropy, one periodic orbit with period 2n for each n≥0, no other periodic orbits, and a single invariant Cantor set which has a continuum of possible but, in any case, simple geometric structures. These diffeomorphisms are Cr(d)-smooth, where r(d) is a strictly increasing function of d, which goes to infinity with d. The second part contains a more general result about smooth maps obtained by an infinite sequence of surgeries, and further particular cases. © 1992 Springer-Verlag.