Kernel of a map of a shift along the orbits of continuous flows |
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Authors: | S I Maksymenko |
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Institution: | 1.Institute of Mathematics,Ukrainian National Academy of Sciences,Kyiv,Ukraine |
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Abstract: | Let F:M ×
\mathbbR \mathbb{R} → M be a continuous flow on a topological manifold M. For every subset V ì M V \subset M , we denote by P(V) the set of all continuous functions
x:V ? \mathbbR \xi :V \to \mathbb{R} such that
\textF( x,x(x) ) = x {\text{F}}\left( {x,\xi (x)} \right) = x for all x ? V x \in V . These functions vanish at nonperiodic points of the flow, while their values at periodic points are integer multiples of
the corresponding periods (in general, not minimal). In this paper, the structure of P(V) is described for an arbitrary connected open subset V ì M V \subset M . |
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Keywords: | |
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