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an expansive homeomorphism of a compact metric space, the theorem of uniform expansivity states that for every
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Positive expansivity is much stronger than expansivity. In fact, one can prove that if
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This article is about mathematical expansivity. For other uses, see
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321:{\displaystyle d(f^{n}(x),f^{n}(y))\geq \varepsilon _{0}.}
801:{\displaystyle d(f^{n}(x),f^{n}(y))\geq \varepsilon _{0}}
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may be expansive in the forward or backward directions.
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This article incorporates material from the following
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162:{\displaystyle \varepsilon _{0}>0,}
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351:can be positive or negative, and so
39:. The idea of expansivity is fairly
1274:: expansive, uniform expansivity.
1038:{\displaystyle \vert n\vert \leq N}
978:{\displaystyle d(x,y)>\epsilon }
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1006:{\displaystyle n\in \mathbb {Z} }
721:{\displaystyle n\in \mathbb {N} }
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644:{\displaystyle \varepsilon _{0}}
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839:{\displaystyle \epsilon >0}
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45:Schwarz–Ahlfors–Pick theorem
18:expansivity (disambiguation)
1259:Expansive dynamical systems
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22:expansion (disambiguation)
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898:such that for each pair
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673:{\displaystyle x\neq y}
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621:) if there is a
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606:{\displaystyle X}
508:{\displaystyle f}
456:{\displaystyle f}
436:{\displaystyle d}
387:{\displaystyle X}
364:{\displaystyle f}
344:{\displaystyle n}
235:{\displaystyle n}
215:{\displaystyle X}
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1268:PlanetMath
1181:Discussion
944:such that
374:The space
51:Definition
1115:δ
1112:−
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996:∈
973:ϵ
854:δ
828:ϵ
790:ε
786:≥
711:∈
665:≠
633:ε
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569::
443:, and if
307:ε
303:≥
187:≠
142:ε
128:expansive
111:→
105::
1282:Category
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495:, then
396:compact
1133:where
816:Given
24:, and
1247:proof
1175:proof
1013:with
555:If
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41:rigid
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846:and
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617:(or
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55:If
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