Standardness of automorphisms of transposition of intervals and fluxes on surfaces

Anatoly Katok; E. A. Sataev

doi:10.1007/BF01098897

Standardness of automorphisms of transposition of intervals and fluxes on surfaces

Anatoly Katok, E. A. Sataev

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Abstract

In this article we shall prove a new necessary and sufficient condition for automorphisms to be standard, from which we shall deduce the standardness of an automorphism of transposition of intervals with respect to any continuous Borel invariant ergodic measure, and the standardness of the flux of the class C¹ on a two-dimensional compact variety with a finite number of stationary points and separatrices, with respect to any Borel invariant ergodic measure whose carrier contains an open set.

Original language	English (US)
Pages (from-to)	826-831
Number of pages	6
Journal	Mathematical Notes of the Academy of Sciences of the USSR
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/BF01098897
State	Published - Oct 1 1976

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF01098897

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AB - In this article we shall prove a new necessary and sufficient condition for automorphisms to be standard, from which we shall deduce the standardness of an automorphism of transposition of intervals with respect to any continuous Borel invariant ergodic measure, and the standardness of the flux of the class C1 on a two-dimensional compact variety with a finite number of stationary points and separatrices, with respect to any Borel invariant ergodic measure whose carrier contains an open set.

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Standardness of automorphisms of transposition of intervals and fluxes on surfaces

Abstract

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