QUASI-INVARIANT MEASURES, ESCAPE RATES AND THE EFFECT OF THE HOLE

被引：8
|
作者：
Bahsoun, Wael [1 ]
Bose, Christopher [2 ]
机构：
[1] Univ Loughborough, Dept Math Sci, Loughborough LE11 3TU, Leics, England
[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 27卷 / 03期
关键词：
Transfer Operator; Interval Maps; Escape Rates; Ulam's Method; EXPANDING MAPS; APPROXIMATION; ENTROPY; CHAOS;
D O I：
10.3934/dcds.2010.27.1107
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let T be a piecewise expanding interval map and T(H) be an abstract perturbation of T into an interval map with a hole. Given a number l, 0 < l < 1, we compute an upper-bound on the size of a hole needed for the existence of an absolutely continuous conditionally invariant measure (accim) with escape rate not greater than - ln(1 - l). The two main ingredients of our approach are Ulam's method and an abstract perturbation result of Keller and Liverani.
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页码：1107 / 1121
页数：15
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