| Summary: | This is a survey paper on selected topics concerning the embeddability of given mappings
in real flows. Particular attention will be paid to the relationship between the problem
of the embeddability and functional equations.Let X be a real manifold and
f:X →
X be a homeomorphism. A family of homeomorphisms
{ft:X →
X,t ∈ R} such thatft°fs
= ft + s
for t,s ∈ R
and f1 =
f is said to be an embedding of
f.
The embedding is of class Cr if for every
x ∈
X the mapping t →
ft(x)
is continuous and all ft are of class
Cr. We concentrate on
the cases where X is an open subset of RN,X is a closed and an open
interval, and X is a circle. We discuss the following problems: the
existence of embeddings with suitable regularity; the conditions which imply the
uniqueness of embeddings; the formulas expressing the above embeddings or their general
constructions.
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