Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/48639
Title: On Deterministic Perturbations of Summability Maps
Authors: GAO BING
Keywords: non-uniformly expanding, perturbations, Jakobson's theorem, summability, Collet-Eckmann condition, asymptotic distribution
Issue Date: 21-Aug-2013
Source: GAO BING (2013-08-21). On Deterministic Perturbations of Summability Maps. ScholarBank@NUS Repository.
Abstract: This thesis contains two topics on perturbations of non-uniformly expanding interval maps. The first topic is to provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family $f_t$ of maps with $f_0=f$, we prove that $t=0$ is a Lebesgue density point of the set of parameters for which $f_t$ satisfies both the Collet-Eckmann condition and a strong polynomial recurrence condition. The second topic is to investigate the asymptotic distributions of the critical orbits. Consider a one-parameter family with some conditions and let E be the set of parameters $t$ for which $f_t$ satisfies a summability condition. We prove that for almost all $t\in E$, each critical points of $f_t$ belongs to one of the ergodic acips.
URI: http://scholarbank.nus.edu.sg/handle/10635/48639
Appears in Collections:Ph.D Theses (Open)

Show full item record
Files in This Item:
File Description SizeFormatAccess SettingsVersion 
GaoB.pdf970.04 kBAdobe PDF

OPEN

NoneView/Download

Page view(s)

151
checked on Dec 11, 2017

Download(s)

165
checked on Dec 11, 2017

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.