# Inhomogeneities in chainable continua

@article{Anuvsic2021InhomogeneitiesIC,
title={Inhomogeneities in chainable continua},
author={Ana Anuvsi'c and Jernej vCinvc},
journal={Fundamenta Mathematicae},
year={2021}
}
• Published 17 February 2020
• Mathematics
• Fundamenta Mathematicae
We study a class of chainable continua which contains, among others, all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of non-hyperbolic surface homeomorphisms. Using dynamical properties of the bonding map, we give conditions for existence of endpoints, characterize the set of local inhomogeneities, and determine when it consists only of endpoints. As a side product we also obtain…
1 Citations

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## References

SHOWING 1-10 OF 47 REFERENCES

### Inhomogeneities in non-hyperbolic one-dimensional invariant sets

The topology of one-dimensional invariant sets (attractors) is of great in- terest. R. F. Williams (20) demonstrated that hyperbolic one-dimensional non-wandering sets can be represented as inverse

### Large derivatives, backward contraction and invariant densities for interval maps

• Mathematics
• 2008
In this paper, we study the dynamics of a smooth multimodal interval map f with non-flat critical points and all periodic points hyperbolic repelling. Assuming that |Dfn(f(c))|→∞ as n→∞ holds for all

### Subcontinua of inverse limit spaces of unimodal maps

• Mathematics
• 1999
We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit

### An arc as the inverse limit of a single nowhere strictly monotone bonding map on [0,1]

Introduction. It is well known that a nondegenerate continuum (compact, connected metric space) is chainable if and only if it is homeomorphic to the limit of an inverse sequence of arcs with bonding

### Prime ends dynamics in parametrised families of rotational attractors

• Mathematics
Journal of the London Mathematical Society
• 2020
We provide several new examples in dynamics on the 2‐sphere, with the emphasis on better understanding the induced boundary dynamics of invariant domains in parametrised families. First, motivated by

### Hofbauer towers and inverse limit spaces

In this paper we use Hofbauer towers for unimodal maps to study the collection of endpoints of the associated inverse limit spaces. It is shown that if f is a unimodal map for which the kneading map

### Inverse limits as attractors in parameterized families

• Mathematics
• 2013
We show how a parameterized family of maps of the spine of a manifold can be used to construct a family of homeomorphisms of the ambient manifold which have the inverse limits of the spine maps as

### On iterated maps of the interval

• Mathematics
• 1988
Introduction. Mappings from an interval to itself provide the simplest possible examples of smooth dynamical systems. Such mappings have been widely studied in recent years since they occur in quite

### Measurable dynamics of $S$-unimodal maps of the interval

• Mathematics
• 1991
— In this paper we sum up our results on one-dimensional measurable dynamics reducing them to the S-unimodal case (compare Appendix 2). Let / be an S-unimodal map of the interval having no limit