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Only rational homology spheres admit Ω(f) to be union of DE attractors

Published online by Cambridge University Press:  04 November 2009

FAN DING ,
JIANZHONG PAN ,
SHICHENG WANG  and
JIANGANG YAO
FAN DING
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: dingfan@math.pku.edu.cn, wangsc@math.pku.edu.cn)
JIANZHONG PAN
Affiliation:
Institute of Mathematics, HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China (email: pjz@amss.ac.cn)
SHICHENG WANG
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: dingfan@math.pku.edu.cn, wangsc@math.pku.edu.cn)
JIANGANG YAO
Affiliation:
Department of Mathematics, University of California at Berkeley, CA 94720, USA (email: jgyao@math.berkeley.edu)
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Abstract

If there exists a diffeomorphism f on a closed, orientable n-manifold M such that the non-wandering set Ω(f) consists of finitely many orientable ( ±) attractors derived from expanding maps, then M is a rational homology sphere; moreover all those attractors are of topological dimension n−2. Expanding maps are expanding on (co)homologies.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 5 , October 2010 , pp. 1399 - 1417
Copyright
Copyright © Cambridge University Press 2009

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