Geometry & Topology
- Geom. Topol.
- Volume 22, Number 4 (2018), 2145-2186.
Rotation intervals and entropy on attracting annular continua
We show that if is an annular homeomorphism admitting an attractor which is an irreducible annular continua with two different rotation numbers, then the entropy of is positive. Further, the entropy is shown to be associated to a –robust rotational horseshoe. On the other hand, we construct examples of annular homeomorphisms with such attractors for which the rotation interval is uniformly large but the entropy approaches zero as much as desired.
The developed techniques allow us to obtain similar results in the context of Birkhoff attractors.
Geom. Topol., Volume 22, Number 4 (2018), 2145-2186.
Received: 18 July 2016
Revised: 22 May 2017
Accepted: 1 October 2017
First available in Project Euclid: 13 April 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 37B40: Topological entropy 37B45: Continua theory in dynamics 37E45: Rotation numbers and vectors 54H20: Topological dynamics [See also 28Dxx, 37Bxx]
Passeggi, Alejandro; Potrie, Rafael; Sambarino, Martín. Rotation intervals and entropy on attracting annular continua. Geom. Topol. 22 (2018), no. 4, 2145--2186. doi:10.2140/gt.2018.22.2145. https://projecteuclid.org/euclid.gt/1523584819