Extending expansive homeomorphisms

Wine, J. D.

doi:10.1090/S0002-9939-1982-0671230-8

Extending expansive homeomorphisms
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by J. D. Wine PDF

Proc. Amer. Math. Soc. 86 (1982), 531-534 Request permission

Abstract:

In previous work on extensions of expansive homeomorphisms there has always been a finiteness condition placed on the remainder. In this note we give a necessary and sufficient condition for a self-homeomorphism to be expansive by restrictions on orbits, and then use this to give a sufficient condition for the homeomorphic extension of an expansive homeomorphism to be expansive. Two examples are given wherein the homeomorphic extensions of expansive homeomorphism are examined relative to the conditions of the theorem.

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