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Stratification of the space of unimodal interval maps

Published online by Cambridge University Press:  19 September 2008

Louis Block  and
David Hart
Louis Block
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611, USA
David Hart
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611, USA
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Abstract

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The space of ‘quadratic-like’ (unimodal) maps of a compact interval to itself is shown to decompose in a ‘nice’ way (stratify) according to a dynamical property of such maps (the existence of a homoclinic periodic orbit with given period). This decomposition is refined by that discovered by Sarkovskii. Orbit structure and bifurcation properties are also discussed.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 3 , Issue 4 , December 1983 , pp. 533 - 539
Copyright
Copyright © Cambridge University Press 1983

References

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