BibTex format
@article{Kozlovski:2019,
author = {Kozlovski, O and Strien, SV},
title = {Asymmetric unimodal maps with non-universal period-doubling scaling laws},
url = {http://arxiv.org/abs/1907.05812v1},
year = {2019}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - JOUR
AB - We consider a family of strongly-asymmetric unimodal maps $\{f_t\}_{t\in[0,1]}$ of the form $f_t=t\cdot f$ where $f\colon [0,1]\to [0,1]$ is unimodal,$f(0)=f(1)=0$, $f(c)=1$ is of the form and $$f(x)=\left\{ \begin{array}{ll}1-K_-|x-c|+o(|x-c|)& \mbox{ for }x<c, \\ 1-K_+|x-c|^\beta + o(|x-c|^\beta)&\mbox{ for }x>c, \end{array}\right. $$ where we assume that $\beta>1$. We showthat such a family contains a Feigenbaum-Coullet-Tresser $2^\infty$ map, anddevelop a renormalization theory for these maps. The scalings of therenormalization intervals of the $2^\infty$ map turn out to besuper-exponential and non-universal (i.e. to depend on the map) and thescaling-law is different for odd and even steps of the renormalization. Theconjugacy between the attracting Cantor sets of two such maps is smooth if andonly if some invariant is satisfied. We also show that theFeigenbaum-Coullet-Tresser map does not have wandering intervals, butsurprisingly we were only able to prove this using our rather detailed scalingresults.
AU - Kozlovski,O
AU - Strien,SV
PY - 2019///
TI - Asymmetric unimodal maps with non-universal period-doubling scaling laws
UR - http://arxiv.org/abs/1907.05812v1
UR - http://hdl.handle.net/10044/1/77852
ER -