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The Jordan Curve‐type Theorems for the Funnel in 2‐dimensional Semiflows
Author(s) -
CIESIELSKI KRZYSZTOF
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36798.x
Subject(s) - funnel , boundary (topology) , mathematics , type (biology) , point (geometry) , manifold (fluid mechanics) , isolated point , periodic point , mathematical analysis , jordan curve theorem , trajectory , physics , geometry , combinatorics , pure mathematics , mathematical physics , quantum mechanics , topological space , chemistry , geology , paleontology , mechanical engineering , organic chemistry , engineering , topological vector space
We investigate “the past” of a nonstationary point x in a semiflow π: ℝ + x M → M on a 2‐manifold M. In a natural way there are defined two boundary trajectories T a and T b ; by the funnel we mean F ( x ) ={ y: π( t , y ) = x for some t } and we put D ( x ) ≈ F ( x )\( T a ∪ T b ). We show that if x is not a point of negative unicity, then D ( x ) is homeomorphic to ℝ 2 . Also, if T is a nonboundary trajectory through x , then D ( x )\ T has two components for a regular point x and D ( x )\ T has two or three components for a periodic point x.