Accessible points of planar embeddings of tent inverse limit spaces

Weak equivalence of primitive matrices is a known invariant arising naturally from the study of inverse limit spaces. Several new invariants for weak equivalence are described. It is proved that a positive dimension group isomorphism is a complete invariant for weak equivalence. For the transition matrices corresponding to periodic kneading sequences, the discriminant is proved to be an invariant when the characteristic polynomial is irreducible. The results have direct application to the topological classification of one-dimensional inverse limit spaces.

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On isotopy and unimodal inverse limit spaces

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2012.32.1245 ◽

2012 ◽

Vol 32 (4) ◽

pp. 1245-1253 ◽

Cited By ~ 3

Author(s):

Henk Bruin ◽

◽

Sonja Štimac ◽

Keyword(s):

Inverse Limit ◽

Inverse Limit Spaces

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Shadowing property for inverse limit spaces

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1992-1097338-x ◽

1992 ◽

Vol 115 (2) ◽

pp. 573-573 ◽

Cited By ~ 14

Author(s):

Liang Chen ◽

Shi Hai Li

Keyword(s):

Inverse Limit ◽

Shadowing Property ◽

Inverse Limit Spaces

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Filters display inverse limit spaces

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.1789451 ◽

2004 ◽

Vol 14 (4) ◽

pp. 963-968 ◽

Cited By ~ 3

Author(s):

Jesús Urías

Keyword(s):

Inverse Limit ◽

Inverse Limit Spaces

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Inverse Limit Spaces Satisfying a Poincaré Inequality

Analysis and Geometry in Metric Spaces ◽

10.1515/agms-2015-0002 ◽

2015 ◽

Vol 3 (1) ◽

Author(s):

Jeff Cheeger ◽

Bruce Kleiner

Keyword(s):

Banach Space ◽

Large Class ◽

Inverse Limit ◽

Poincaré Inequality ◽

Doubling Condition ◽

Poincare Inequality ◽

Inverse Limit Spaces ◽

Inverse Systems ◽

Nikodym Property

Abstract We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces, and a large class of new examples. As follows easily from [4], generically our examples have the property that they do not bilipschitz embed in any Banach space with Radon-Nikodym property. For Laakso spaces, thiswas noted in [4]. However according to [7] these spaces admit a bilipschitz embedding in L1. For Laakso spaces, this was announced in [5].

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