[Todos CMAT] Seminario de Sistemas Dinámicos viernes 24 de agosto.

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Jue Ago 23 13:51:40 -03 2018


este viernes habla Braulio Augusto Gracia de la UNIFEI (Itajubá, Brasil). Siguen título y resumen.
Title: Forcing relation on the set of periodic orbits of a rotational horseshoe

Given a discrete dynamical system and information about one of its periodic orbits,

can one derive the existence of other periodic orbits, or that it has positive topological entropy?

This is the notion of dynamical order or forcing relation. The classical example of forcing results is the Sharkovski's theorem for self-maps of the real line: 

it defines a total order $succeq$ on the positive integers with the property that

if $msucceq n$ then any continuous self-map of $mathbb{R}$ which has a periodic orbit of period $m$ must also have a periodic orbit of period $n$.

In analogy to the period specification in the Sharkovski’s theorem, Boyland (1988) introduced the braid type of periodic orbits and a (partial) order on the set of braid types.

This is related to Nielsen-Thurston classification of surface homeomorphisms- a periodic orbit $P$ forces another periodic orbit $Q$, $P succeq Q$, if the topological type of $Q$ is achieved by a periodic orbit of the Thurston-Nielsen representative of $f$ relative to $P$.

In this talk, we present results for the Boyland's order on the set of braid types of periodic orbits of a rotational horseshoe on the annulus. 
The forcing relation among these orbits (Boyland's family) is given by the inclusion order on their rotation sets.

This is a join work with Juan Valentín, Unifei.
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