[Todos CMAT] Seminario Dinámica este Viernes.

[Rafael Potrie]

Hola todos,

Este viernes a las 14.30 (en el IMERL) escucharemos a Gabriel Fuhrmann (TU
Dresden, Alemania) que nos hablará acerca de "Non-smooth saddle-node
bifurcations of quasi-periodically forced interval maps". Abajo les dejo el
resumen de su charla. Son todos bienvenidos.

sds


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Non-smooth saddle-node bifurcations of quasi-periodically forced interval
maps

ABSTRACT: This talk deals with quasi-periodically forced interval maps of
the form

f: S^1 x R \to S^1 x R
(\theta, x) |---> (\theta + \omega, g(\theta,x) ) with irrational \omega.

 In particular, we focus on bifurcations of the corresponding invariant
graphs of such systems, that is, bifurcations of measurable functions \psi:
S^1 --> R which satisfy:

\psi (\theta + \omega) = g(\theta, \psi(\theta))

We consider the case where the functions g(\theta,\cdot) are monotonously
increasing and concave. In this situation, we provide sufficient conditions
for a family of forced maps to undergo a non-smooth saddle-node
bifurcation. In contrast to former results in this direction, our
conditions are C^2-open in the set of families with fixed Diophantine
rotation number \omega. Further, we answer a question by Herman on the
topological structure of the minimal set at the bifurcation. A similar
result has earlier been derived by Bjerkl\"{o}v for the special case of a
projective dynamical system associated to a quasi-periodic Schr\"{o}dinger
cocycle. We provide a simplified proof of an extension of his result to
systems of the above form. Finally, we compute the Hausdorff dimension of
the upper bounding graph of the minimal set at the bifurcation.




-- 
Rafael Potrie
rafaelpotrie en gmail.com
http://www.cmat.edu.uy/~rpotrie/
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