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Mat. Sb., 2015, Volume 206, Number 4, Pages 99–130 (Mi msb8295)  

Mixing and eigenfunctions of singular hyperbolic attractors

E. A. Sataev

Obninsk Institute for Nuclear Power Engineering of the National Research Nuclear University MEPhI

Abstract: 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.
Bibliography: 28 titles.

Keywords: singular hyperbolic attractor, invariant measure, mixing, eigenfunction.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00666
Ministry of Education and Science of the Russian Federation НШ-5998.2012.1
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 13-01-00666) and the Programme for the Support of Leading Scientific Schools of the Russian Federation (grant no. НШ-5998.2012.1).


DOI: https://doi.org/10.4213/sm8295

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English version:
Sbornik: Mathematics, 2015, 206:4, 572–599

Bibliographic databases:

UDC: 517.938
MSC: Primary 37A25, 37C70, 37D99; Secondary 37D10
Received: 28.10.2013 and 22.01.2015

Citation: E. A. Sataev, “Mixing and eigenfunctions of singular hyperbolic attractors”, Mat. Sb., 206:4 (2015), 99–130; Sb. Math., 206:4 (2015), 572–599

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