圆的粗糙变换的笛卡尔积上的悬架

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI:10.1134/S1061920824601794

E. Nozdrinova, O. Pochinka, V. Shmukler, S. Zinina

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引用次数: 0

摘要

在流形上求流的构造之一是在微分同态上构造悬架。S. Smale证明了共轭微分同态上的悬架是拓扑等价的。相反的情况在一般情况下是不成立的。这一事实的一个经典例证是悬架相等的圆的非共轭微分同态的例子。本文建立了圆的粗糙变换的笛卡尔积的拓扑共轭不变量与悬架的拓扑等价不变量之间的关系。DOI 10.1134 / S1061920824601794

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On Suspensions over Cartesian Products of Rough Transformations of the Circle

One of the constructions for obtaining flows on a manifold is the construction of a suspension over a diffeomorphism. S. Smale showed that suspensions over conjugate diffeomorphisms are topologically equivalent. The converse is not true in the general case. A classic illustration of this fact are examples of nonconjugate diffeomorphisms of a circle whose suspensions are equivalent. In this paper, we establish relations between the invariants of topological conjugacy of Cartesian products of rough transformations of a circle and the invariants of topological equivalence of suspensions over them.

DOI 10.1134/S1061920824601794

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.