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Subjects
37-XX Dynamical systems and ergodic theory
37Exx Low-dimensional dynamical systems
37E99 None of the above, but in this section

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Homeomorphisms of inverse limit spaces of one-dimensional maps

Marcy Barge, Beverly Diamond (1995)

Fundamenta Mathematicae

We present a new technique for showing that inverse limit spaces of certain one-dimensional Markov maps are not homeomorphic. In particular, the inverse limit spaces for the three maps from the tent family having periodic kneading sequence of length five are not homeomorphic.

Hyperbolicity in a class of one-dimensional maps.

Gregory J. Davis (1990)

Publicacions Matemàtiques

In this paper we provide a direct proof of hyperbolicity for a class of one-dimensional maps on the unit interval. The maps studied are degenerate forms of the standard quadratic map on the interval. These maps are important in understanding the Newhouse theory of infinitely many sinks due to homoclinic tangencies in two dimensions.

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