4 papers
Maps in Dimension One with Infinite Entropy
Peter Hazard
We give examples of endomorphisms in dimension one with infinite topological entropy which are -Hölder and -Sobolev for all and . This is const…
Genericity of Infinite Entropy for Maps with Low Regularity
Edson de Faria, Peter Hazard, Charles Tresser
For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the…
Infinitely Many Moduli of Stability at the Dissipative Boundary of Chaos
Peter Hazard, Marco Martens, Charles Tresser
In the family of area-contracting Hénon-like maps with zero topological entropy we show that there are maps with infinitely many moduli of stability. Thus one cannot find all the p…
Braid Equivalence in the Hénon Family I
André de Carvalho, Toby Hall, Peter Hazard
We give two general constructions of braid equivalences which exist between certain deformations of the 2-branched Horsehoe map. We then give numerical evidence suggesting that the…