Nesta sexta-feira (11/09) teremos mais um encontro do Seminário de Sistemas Dinâmicos da UFF, dessa vez com sessão dupla!
Seguem abaixo os detalhes:
14h30 Rubio Gunawan The (SISSA, Italia)
Title: Counterintuitive Attractors in One Dimension: Wild Attractors and
Sisyphus Attractors
Abstract: We present two recent results on C-infinity full branch maps
that exhibit interesting counterintuitive behavior on their attractors.
We will also discuss the key ideas and how the two results connect.
The first result is the existence of C-infinity full branch maps with
infinite branches, uniformly expanding, but almost every point converges
to 0. Furthermore, the basin of attraction is meagre, so 0 is an example
of a wild attractor.
The second result is the existence of C-infinity two-to-one circle
coverings where 0 is a hyperbolic repelling fixed point, but it is also
a statistical attractor (i.e. it supports a physical measure). We coin
the term sisyphus attractor to describe the behavior of this point.
15h30 Tanja Schindler (Exeter, Reino Unido e Jagiellonian, Polônia)
Title: Trimmed sums, extravagances and extreme historic behaviour
Abstract: We consider an irrational rotation R_α on the torus (R_α(x)=
x+α mod 1) and the non-integrable observable f(x)=1/x-1/(1-x) and study
the Birkhoff sum S_n=f+…+f(R_α^(n-1)). As by Aaronson’s theorem it is
not possible to obtain strong convergence for S_n/d_n where d_n is any
norming sequence, we look at the trimmed sum where we delete one or more
of the maximal terms to obtain strong convergence. Depending on the
Diophantine properties of α we may need to delete only one or many of
the maximal entries of the Birkhoff sum to obtain strong convergence.
Moreover, we look at extravagance, i.e. the limsup behaviour of f(R_α^n)
/ S_n and show under which conditions it equals ∞ or 0. These results
have consequences in studying a reparametrization (T_t) of the linear
flow (L_t) with direction (1,α) on the two torus T2 with function φ,
where φ is a smooth non-negative function that has exactly two
(non-degenerate) zeros at p and q. We prove that for a full measure set
(α,p,q)∈ T×T^2×T^2 the special flow (T_t) exhibits extreme historic
behavior proving a conjecture given by Andersson and Guihéneuf. The talk
is based on joint work with Max Auer and with Adam Kanigowski.
Os seminários serão realizados na sala 409 (Bloco H, Gragoatá).
Esperamos vocês!