Algorithmic information for intermittent systems with an indifferent fixed point

Infinite mixing for one-dimensional maps with an indifferent fixed point

We study the properties of `infinite-volume mixing' for two classes of intermittent maps: expanding maps $[0,1] \longrightarrow [0,1]$ with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding maps $\mathbb{R}^+ \longrightarrow \mathbb{R}^+$ with an indifferent fixed point at $+\infty$ preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of syste…

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。

A simple proof of the exactness of expanding maps of the interval with an indifferent fixed point

Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0,1], with countably many surjective branches and a strongly neutral fixed point in 0.

具有临界点和奇异点的双重间歇全分支映射

Doubly Intermittent Full Branch Maps with Critical Points and Singularities

研究一类具有两个中性不动点及临界点或奇异点的一维全分支映射，在温和假设下证明唯一混合绝对连续不变测度存在，并分析其相关衰减与极限定理。

Statistical properties of intermittent maps with unbounded derivative

We study the ergodic and statistical properties of a class of maps of the circle and of the interval of Lorenz type which present indifferent fixed points and points with unbounded derivative. These maps have been previously investigated in the physics literature. We prove in particular that correlations decay polynomially, and that suitable Limit Theorems (convergence to Stable Laws or Central Limit Theorem) hold for Hölder continuous observables. We moreover show that the return and hitting times are in the limit exponentially distributed.

Distributional behavior of time averages of non-$L^1$ observables in one-dimensional intermittent maps with infinite invariant measures

In infinite ergodic theory, two distributional limit theorems are well-known. One is characterized by the Mittag-Leffler distribution for time averages of $L^1(m)$ functions, i.e., integrable functions with respect to an infinite invariant measure. The other is characterized by the generalized arc-sine distribution for time averages of non-$L^1(m)$ functions. Here, we provide another distributional behavior of time averages of non-$L^1(m)$ functions in one-dimensional intermittent maps where each has an indifferent fixed point and an infinite invariant measure. Observation functions considered…