Rotation number

Known as: Map winding number 
In mathematics, the rotation number is an invariant of homeomorphisms of the circle.
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1970-2017
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2010
2010
Article history: Received 17 April 2009 Revised 28 October 2009 Available online 11 November 2009 MSC: 60H10 34F05 37H10 
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2009
2009
We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the… (More)
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2008
2008
We study how parallel chip-firing on the complete graph Kn changes behavior as we vary the total number of chips. Surprisingly… (More)
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2008
2008
In this paper we present a numerical method to compute derivatives of the rotation number for parametric families of circle… (More)
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2008
2008
We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle… (More)
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2004
2004
(The analysis leading to these equat ions will be out l ined in Sect ion 2.) Here, a is a n u m b e r and g (x ) a funct ion def… (More)
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2002
2002
The self-rotation number, as defined by Peckham, is the rotation rate of the image of a point about itself. Here we use the… (More)
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1999
1999
In generalizing the classical theory of circle maps, we study the rotation set for maps of the real line x 7 ! f(x) with almost… (More)
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1996
1996
We consider the rotation set ρ(F ) for a lift F of an area preserving homeomorphism f : T → T, which is homotopic to the identity… (More)
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1986
1986
We construct asymptotic expansions for the exponential growth rate (Lyapunov exponent) and rotation number of the random… (More)
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