ICTP Dynamical Systems Seminars - Tuesday, 28 March 2023, 15:00 - 17:30 - (VENUE: Fibonacci Lecture Room - Galileo Guest House)

[ICTP Math Section]

_Dynamical Systems Seminars __
_
Venue: Fibonacci Lecture Room (Galileo Guest House)

Tuesday, 28 March 2023 (15:00 - 17:30)

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_15:00: *Giovanni Panti* (University of Udine)

Title:*Attractors of dual continued fractions*

*Abstract:* Given a Farey-type map F with full branches in the extended 
Hecke group Gamma_m, its dual F_# results from constructing the natural 
extension of F, letting time go backwards, and projecting. Although 
numerical simulations may suggest otherwise, we show that the domain of 
F_# is always tame, that is, it always contains intervals. As a main 
technical tool we construct, for every m=3,4,5,..., a homeomorphism M_m 
that simultaneously linearizes all maps with branches in Gamma_m, and 
show that the resulting dual linearized iterated function system 
satisfies the strong open set condition. We explicitly compute the 
Holder exponent of every M_m, generalizing Salem's results for the 
Minkowski question mark function M_3.


16:15: *Ayreena Bakhtawar* (Scuola Normale Superiore di Pisa)

Title:*Improvements to Dirichlet's theorem in Diophantine approximation*

*Abstract: *Diophantine Approximation is a branch of Number Theory in 
which the central theme is understanding how well real numbers can be 
approximated by rationals. Dirichlet’s theorem (1842) is a fundamental 
result that gives an optimal approximation rate of any irrational 
number. The set of real numbers for which Dirichlet's theorem admits an 
improvement was originally studied by Davenport and Schmidt. In this 
talk I will discuss some new metrical results for the set of Dirichlet 
improvable numbers.

Everyone is welcome to attend


-- 

Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

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