Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities

• Autorzy: Chris Good , Robin Knight , Brian Raines
• Języki publikacji: EN

Abstrakty

EN

We examine the structure of countable closed invariant sets under a dynamical system on a compact metric space. We are motivated by a desire to understand the possible structures of inhomogeneities in one-dimensional nonhyperbolic sets (inverse limits of finite graphs), particularly when those inhomogeneities form a countable set. Using tools from descriptive set theory we prove a surprising restriction on the topological structure of these invariant sets if the map satisfies a weak repelling or attracting condition. We show that for a family of conceptual models for the Hénon attractor, inverse limits of tent maps, these restrictions characterize the structure of inhomogeneities. We end with several results regarding the collection of parameters that generate such spaces.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54F15: Continua and generalizations
• 37B45: Continua theory in dynamics
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 192
• Numer: 3
• Strony: 267-289

Daty

wydano

2006

Twórcy

autor

Chris Good

• School of Mathematics and Statistics, University of Birmingham, Birmingham, B15 2TT, UK

autor

Robin Knight

• Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK

autor

Brian Raines

• Department of Mathematics, Baylor University, Waco, TX 76798-7328, U.S.A.

Identyfikatory

DOI

10.4064/fm192-3-6