On the classes of Lipschitz and smooth conjugacies of unimodal maps

Waldemar Pałuba. "On the classes of Lipschitz and smooth conjugacies of unimodal maps." Fundamenta Mathematicae 183.3 (2004): 215-227. <http://eudml.org/doc/282615>.

@article{WaldemarPałuba2004,
abstract = {Under very mild assumptions, any Lipschitz continuous conjugacy between the closures of the postcritical sets of two C¹-unimodal maps has a derivative at the critical point, and also on a dense set of its preimages. In a more restrictive situation of infinitely renormalizable maps of bounded combinatorial type the Lipschitz condition automatically implies the C¹-smoothness of the conjugacy. Here the critical degree can be any real number α > 1.},
author = {Waldemar Pałuba},
journal = {Fundamenta Mathematicae},
keywords = {-unimodal maps; Lipschitz condition; -smoothness; conjugacy},
language = {eng},
number = {3},
pages = {215-227},
title = {On the classes of Lipschitz and smooth conjugacies of unimodal maps},
url = {http://eudml.org/doc/282615},
volume = {183},
year = {2004},
}

TY - JOUR
AU - Waldemar Pałuba
TI - On the classes of Lipschitz and smooth conjugacies of unimodal maps
JO - Fundamenta Mathematicae
PY - 2004
VL - 183
IS - 3
SP - 215
EP - 227
AB - Under very mild assumptions, any Lipschitz continuous conjugacy between the closures of the postcritical sets of two C¹-unimodal maps has a derivative at the critical point, and also on a dense set of its preimages. In a more restrictive situation of infinitely renormalizable maps of bounded combinatorial type the Lipschitz condition automatically implies the C¹-smoothness of the conjugacy. Here the critical degree can be any real number α > 1.
LA - eng
KW - -unimodal maps; Lipschitz condition; -smoothness; conjugacy
UR - http://eudml.org/doc/282615
ER -