top
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.
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 -