Mixing and eigenfunctions of singular hyperbolic attractors

被引：0
|
作者：
Sataev, E. A. [1 ]
机构：
[1] Obninsk Inst Nucl Power Engn, Obninsk, Russia
来源：
SBORNIK MATHEMATICS | 2015年 / 206卷 / 04期
基金：
俄罗斯基础研究基金会;
关键词：
singular hyperbolic attractor; invariant measure; mixing; eigenfunction; AXIOM;
D O I：
10.1070/SM2015v206n04ABEH004470
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is concerned with investigating singular hyperbolic flows. It is shown that an eigenfunction cannot be continuous on an ergodic component containing a fixed point. However, it is continuous on a certain set (after a modification on a nullset). The following alternative is established: either there exists an eigenfunction on an ergodic component or the flow is mixing on this component. Sufficient conditions for mixing are given.
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页码：572 / 599
页数：28
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