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Asymptotic Cycles on Non‐Compact Spaces
Author(s) -
Schwartzman Sol
Publication year - 1997
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/s0024609396002561
Subject(s) - mathematics , measure (data warehouse) , compact space , probability measure , class (philosophy) , mathematics subject classification , invariant (physics) , pure mathematics , invariant measure , set (abstract data type) , mathematical analysis , ergodic theory , database , artificial intelligence , computer science , mathematical physics , programming language
The notion of an asymptotic cycle is extended to flows on non‐compact spaces, and it is proved that for a suitable class of flows on manifolds it is true that the set of points with asymptotic cycles defined has measure one with respect with every invariant probability measure. 1991 Mathematics Subject Classification 58F25.