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

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...

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Publisher copy:
10.4064/fm192-3-6

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Journal:
Fundamenta Mathematicae
Volume:
192
Issue:
3
Pages:
267-289
Publication date:
2006
DOI:
EISSN:
1730-6329
ISSN:
0016-2736
URN:
uuid:0e50df39-0725-4280-ba4b-22ae86fee2b7
Source identifiers:
12848
Local pid:
pubs:12848

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