Expansive View Of The Tule Lake Basin
Expansivity may refer to: * Expansive homeomorphism * Expansive Poetry * Expansive clay Expansive clay is a clay soil that is prone to large volume changes (swelling and shrinking) that are directly related to changes in water content. Soils with a high content of expansive minerals can form deep cracks in drier seasons or years; su ... * Expansive Catasetum * Expansive drill bit * Expansive Heart See also * Expansion (other) {{disambiguation ...
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Expansive Homeomorphism
In mathematics, the notion of expansivity formalizes the notion of points moving away from one another under the action of an iterated function. The idea of expansivity is fairly rigid, as the definition of positive expansivity, below, as well as the Schwarz–Ahlfors–Pick theorem demonstrate. Definition If (X,d) is a metric space, a homeomorphism f\colon X\to X is said to be expansive if there is a constant :\varepsilon_0>0, called the expansivity constant, such that for every pair of points x\neq y in X there is an integer n such that :d(f^n(x),f^n(y))\geq\varepsilon_0. Note that in this definition, n can be positive or negative, and so f may be expansive in the forward or backward directions. The space X is often assumed to be compact Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilize ...
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