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The bifurcation of homoclinic orbits of maps of the interval

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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Relationships involving homoclinic orbits of various periods and the Sarkovskii stratification are given and corresponding bifurcation properties are derived. It is shown that if a continuous map has one homoclinic periodic orbit, it has infinitely many. In any family of C1 maps going from zero to positive entropy, infinitely many homoclinic bifurcations occur, involving periods which are successively smaller powers of two.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 2 , June 1982 , pp. 131 - 138
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

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