Decreasing families of dynamically determined intervals in the power-law family
| dc.creator | Paluba, Waldemar | |
| dc.date | 2007-04-11 | |
| dc.date.accessioned | 2026-07-07T07:56:08Z | |
| dc.date.available | 2026-07-07T07:56:08Z | |
| dc.description | We study the rate of growth of ratios of intervals delimited by the post-critical orbit of a map in the quasi-quadratic family $x\mapsto -|x|^α+a.$ The critical order $α$ is an arbitrary real number $α>1.$ The range of the parameter $a$ is confined to an interval $(1,a_α)$ of length depending on the critical order. We prove that in every power-law family there is a unique parameter $p_α$ corresponding to the kneading sequence $RLRRRLRC.$ Subsequently, we obtain monotonicity results concerning ratios of all intervals labeled by infinite post-critical orbit in the case of the kneading sequence $RLRL...$ This extends the results from \cite{P}, via refinement of the tools based on special properties of power-law mappings in non-euclidean metric. | |
| dc.identifier | https://arxiv.org/abs/0704.1385 | |
| dc.identifier | http://arxiv.org/abs/0704.1385 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127198 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37D05 | |
| dc.title | Decreasing families of dynamically determined intervals in the power-law family | |
| dc.type | text |