2 citations · 4 across the 5 of their papers we have counts for
9 papers
Generalized Whitney Topologies are Baire
Edson de Faria, Peter Hazard
In this paper we show that certain generalizations of the -Whitney topology, which include the Hölder-Whitney and Sobolev-Whitney topologies on smooth manifolds, satisfy the B…
Quadratic Irrationals, Closed Geodesics on the Modular Surface and Dynamical Zeta Functions
Peter Hazard
We show that generating functions associated to the sequence of convergents of a quadratic irrational are related in a natural way to the dynam- ical zeta function of a hyperbolic…
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…
Quadratic Irrationals, Generating Functions, and Lévy Constants
Anna Belova, Peter Hazard
We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer c…
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…