2012/08/23 by Farinelli, Eglantine
#37C15 #37C85 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1208.4771
In this paper we consider the conjugacy classes of diffeomorphisms of the interval, endowed with the C1-topology. We present several results in the spirit of the one below : Given two diffeomorphisms f,g of the interval [0;1] without hyperbolic fixed point, we give a complete answer to the two following questions: - under what conditions does there exist a sequence of smooth conjugates hn f hn-1 of f tending to g in the C1-topology ? - under what conditions does there exist a continuous path of C1-diffeomorphisms ht such that ht f ht-1 tends to g in the C1 topology ? We present also some consequences of these results as regards the study of the C1-centralizers of C1-contractions of [0;+∞[ ; for instance we exhibit a C1-contraction whose centralizer is uncountable and abelian, but is not a flow.