# Metric cycles, curves and solenoids

1 引用 (Scopus)

### 抄録

We prove that every one-dimensional real Ambrosio-Kirchheim current with zero boundary (i.e. a cycle) in a lot of reasonable spaces (including all finite-dimensional normed spaces) can be represented by a Lipschitz curve parameterized over the real line through a suitable limit of Cesàro means of this curve over a subsequence of symmetric bounded intervals (viewed as currents). It is further shown that in such spaces, if a cycle is indecomposable, i.e. does not contain "nontrivial" subcycles, then it can be represented again by a Lipschitz curve parameterized over the real line through a limit of Cesàro means of this curve over every sequence of symmetric bounded intervals, that is, in other words, such a cycle is a solenoid.

元の言語 English 1443-1463 21 Discrete and Continuous Dynamical Systems- Series A 34 4 https://doi.org/10.3934/dcds.2014.34.1443 Published - 2014 4 Yes

Solenoid
Solenoids
Cycle
Metric
Curve
Real Line
Lipschitz
Interval
Normed Space
Subsequence
Zero

### ASJC Scopus subject areas

• Analysis
• Discrete Mathematics and Combinatorics
• Applied Mathematics

### これを引用

Metric cycles, curves and solenoids. / Gueorguiev, Vladimir Simeonov; Stepanov, Eugene.

：: Discrete and Continuous Dynamical Systems- Series A, 巻 34, 番号 4, 04.2014, p. 1443-1463.

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