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

[Rafael Potrie]

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From: <apasseggi en cmat.edu.uy>
Date: jue., 23 ago. 2018 14:02
Subject: [Todos CMAT] Seminario de Sistemas Dinámicos viernes 24 de agosto.
To: <todos en cmat.edu.uy>, <todos en imerl.edu.uy>


Buenas,

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 $m\succeq n$ 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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