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National Repository of Grey Literature 1 records found  Search took 0.00 seconds. 
Rotation Number on a Circle
 Bíma, Jan ; Vejnar, Benjamin (advisor) ; Pražák, Dalibor (referee)
We apply the dynamical method to obtain structural results concerning certain classes of one-dimensional maps. The notion central to the work is that of a rotation number on a circle; we relate the rotation modulus to periodicity of an orientation-preserving circle homeomorphism and generalize the concept to continuous degree-1 circle maps. We investigate the asymptotic orbit behaviour of circle homeomorphisms with irrational rotation number and develop the Poincaré Classification Theorem which establishes topo- logical (semi-)conjugacy of a circle homeomorphism with an irrational rotation number to a rotation with the same rotation number. 1
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