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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The largeness of sets of points
with non-dense orbit in basic sets on surfaces


Author: Yong Moo Chung
Journal: Proc. Amer. Math. Soc. 124 (1996), 1615-1624
MSC (1991): Primary 58F15
MathSciNet review: 1307504
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Abstract: We show that if $f$ is a diffeomorphism of a closed surface and $\varLambda $ is a basic set for $f$, then $HD(\{x\in \varLambda :the \enspace orbit \enspace of \enspace x \enspace by \enspace f \enspace is \enspace not \enspace dense \enspace in \enspace \varLambda \} )=HD(\varLambda )$.


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Additional Information

Yong Moo Chung
Affiliation: Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo, 192-03 Japan
Email: chong@math.metro-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03215-7
PII: S 0002-9939(96)03215-7
Received by editor(s): August 8, 1994
Received by editor(s) in revised form: November 3, 1994
Communicated by: Mary Rees
Article copyright: © Copyright 1996 American Mathematical Society