Spectral degeneracy and escape dynamics for intermittent maps with a hole

Escape Rates and Singular Limiting Distributions for Intermittent Maps with Holes

We study the escape dynamics in the presence of a hole of a standard family of intermittent maps of the unit interval with neutral fixed point at the origin (and finite absolutely continuous invariant measure). Provided that the hole (is a cylinder that) does not contain any neighborhood of the origin, the surviving volume is shown to decay at polynomial speed with time. The associated polynomial escape rate depends on the density of the initial distribution, more precisely, on its behavior in the vicinity of the origin. Moreover, the associated normalized push forward measures are proved to c…

Slow and fast escape for open intermittent maps

If a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of intermittent maps with a family of slowly mixing measures. We show that there are three regimes: 1) standard hyperbolic-like behavior where the rate of mixing is faster than the rate of escape through the hole, there is a unique limiting absolutely continuous conditionally invariant measure (accim) and there is a complete thermodynamic description of the dynamics on the survivor set; 2) an intermediate regime, where the rate of mixing and escape …

关于间歇映射中围绕惰性固定点收缩孔的逃逸率

On the escape rate for intermittent maps with holes shrinking around the indifferent fixed point

本文研究了间歇映射中围绕惰性固定点收缩孔的逃逸率，通过转移算子分析了开放系统的渐进行为。

Escape rate scaling in infinite measure preserving systems

We investigate the scaling of the escape rate from piecewise-linear dynamical systems displaying intermittency due to the presence of an indifferent fixed-point. Strong intermittent behaviour in the dynamics can result in the system preserving an infinite measure. We define a neighbourhood of the indifferent fixed point to be a hole through which points escape and investigate the scaling of the rate of this escape as the length of the hole decreases, both in the finite measure preserving case and infinite measure preserving case. In the infinite measure preserving systems we observe logarithmi…