[Todos CMAT] Seminario de Dinámica del Viernes 24 de Agosto

[Pablo Lessa]

Hola a todos,

Habrá *seminario de dinámica* mañana *Viernes 24* de Agosto a las *14:30*
en el salón de seminarios del *IMERL*.

A partir de las 14hrs habrá café y galletitas.

Nos hablará *Braulio Augusto Garcia* sobre *Forcing en herraduras
rotacionales*.

Saludos,

Pablo

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*Resumen:*

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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