1976
DOI: 10.1007/bf01437864
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Nonsingular saddle points and the absence of mixing

Abstract: For abstract special flows a sufficient condition of absence of mixing is obtained. The result obtained applies to certain classes of smooth flows with nonsingular fixed points on compact orientable surfaces.

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Cited by 30 publications
(24 citation statements)
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“…That mixing was indeed possible in the latter context was proved in a particular case by Khanin and Sinai [32]. Absence of mixing in the case of Morse forms was obtained by Kochergin in some particular cases [18] (see also [22]), and later generalized to a typical one form by Ulcigrai [35].…”
Section: Introductionmentioning
confidence: 82%
“…That mixing was indeed possible in the latter context was proved in a particular case by Khanin and Sinai [32]. Absence of mixing in the case of Morse forms was obtained by Kochergin in some particular cases [18] (see also [22]), and later generalized to a typical one form by Ulcigrai [35].…”
Section: Introductionmentioning
confidence: 82%
“…Note that, as follows from [3], if the invariant measure on T 2 has a smooth positive density, then the singularities of a "roof" function of the special flow are strictly logarithmic.…”
Section: To the Anniversary Of Anatole Katok My Friend And Teachermentioning
confidence: 99%
“…V. I. Arnold has shown that there exists a smooth closed curve transversal to the orbits of the ergodic component. The invariant measure and the flow naturally induce a smooth parameterization on the curve (this procedure was described in detail, e.g., in [3]). The first-return map is determined everywhere on the curve, except for a finite number of points that are the points of the last intersection of the stable separatrices with the curve.…”
Section: To the Anniversary Of Anatole Katok My Friend And Teachermentioning
confidence: 99%
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“…On the other hand, if the section map happens to be a rotation then any flow with only non-degenerate saddles is not mixing [92].…”
Section: Flows On Surfaces Of Higher Genusmentioning
confidence: 99%