Perturbations of weakly expanding critical orbits

Details Perturbations of weakly expanding critical orbits Perturbations of weakly expanding critical orbits

2011-11-27

arxiv.org/abs/1111.6270v1

Mathematics

Dynamical Systems

Scientific paper

Let f be a polynomial or a rational function, which has r summable critical
points. We prove that there exists an r-dimensional manifold in an appropriate
space containing f, such that, for every smooth curve in it through f, the
ratio between parameter and dynamical derivatives along forward iterates of at
least one summable point tends to a non-zero number.

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