Op amp integrator

2013-12-14T14:57:25Z

91.180.188.40:

{{Underlinked|date=January 2013}}

'''Suspension''' is a construction passing from a map to a flow. Namely, let <math>X</math> be a metric space, <math>f:X\to X</math> be a continuous map and <math>r:X\to\mathbb{R}^+</math> be a function (roof function or ceiling function) bounded away from 0. Consider the quotient space

:<math>X_r=\{(x,t):0\le t\le r(x),x\in X\}/(x,r(x))\sim(fx,0). </math>

The suspension of <math>(X,f)</math> with roof function <math>r</math> is the semiflow<ref>M. Brin and G. Stuck, ''Introduction to Dynamical Systems'', Cambridge University Press, 2002.</ref> <math>f_t:X_r\to X_r</math> induced by the time-translation <math>T_t:X\times\mathbb{R}\to X\times\mathbb{R}, (x,s)\mapsto (x,s+t)</math>.

If <math>r(x)\equiv 1</math>, then the quotient space is also called the [[mapping torus]] of <math>(X,f)</math>.

==References==

{{Reflist}}



[[Category:Dynamical systems]]

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Op amp integrator