Abstract
A function is said to be C1-embeddable if there exists a C1-flow (iteration group)
such that
. The C1-embeddability on a compact interval I is a rare property. It is known that even
-diffeomorphisms with two hyperbolic fixed points need not be C1-embeddable. However, every
-diffeomorphism, for
, with one hyperbolic fixed point is uniquely embeddable in a
-flow. We consider the problem how to correct a given diffeomorphism with two hyperbolic fixed points making it C1-embeddable. We prove that if
,
in
and 0 and 1 are hyperbolic fixed points, then for every
and
and every diffeomorphism g such that
,
and
for a suitable chosen
there exists a unique C1-embeddable function
such that
in
and
in
. We determine the coefficient
and we give a necessary and sufficient condition for the best C1-embeddable approximation of f that is such that g = f.