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Chaotic Homeomorphisms of R n , Lifted from Torus Homeomorphisms
Author(s) -
Alpern Steve,
Prasad V. S.
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460939800561x
Subject(s) - mathematics , torus , rotation number , chaotic , pure mathematics , space (punctuation) , rotation (mathematics) , periodic orbits , zero (linguistics) , combinatorics , topology (electrical circuits) , discrete mathematics , mathematical analysis , geometry , linguistics , philosophy , artificial intelligence , computer science
We establish the existence of self‐homeomorphisms of R n , n ⩾ 2, which are chaotic in the sense of Devaney, preserve volume and are spatially periodic. Moreover, we show that in the space of volume‐preserving homeomorphisms of the n ‐torus with mean rotation zero, those with chaotic lifts to R n are dense, with respect to the uniform topology. An application is given for fixed points of 2‐dimensional torus homeomorphisms (Conley–Zehnder–Franks Theorem). 1991 Mathematics Subject Classification 54H20.