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

Chris Good, Robin Knight, and Brian Raines. "Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities." Fundamenta Mathematicae 192.3 (2006): 267-289. <http://eudml.org/doc/282670>.

@article{ChrisGood2006,
abstract = {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.},
author = {Chris Good, Robin Knight, Brian Raines},
journal = {Fundamenta Mathematicae},
keywords = {attractor; invariant set; inverse limits; unimodal; continuum; indecomposable},
language = {eng},
number = {3},
pages = {267-289},
title = {Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities},
url = {http://eudml.org/doc/282670},
volume = {192},
year = {2006},
}

TY - JOUR
AU - Chris Good
AU - Robin Knight
AU - Brian Raines
TI - Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities
JO - Fundamenta Mathematicae
PY - 2006
VL - 192
IS - 3
SP - 267
EP - 289
AB - 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.
LA - eng
KW - attractor; invariant set; inverse limits; unimodal; continuum; indecomposable
UR - http://eudml.org/doc/282670
ER -