The dynamics of billiards has been studied in great detail when the reflection law is the specular one, i.e., when the angle of reflection equals the angle of incidence. In this talk, I will be concerned with polygonal billiards with a contracting…

# Categoria evento: Dynamical Systems Seminar

## Dynamical Systems Stemming from a Family of Multi-dimensional Continued Fraction Algorithms – Thomas Garrity (Williams College)

The underlying dynamics behind classical continued fractions has been heavily studied. Attempts to generalize the many properties of continued fractions fall under the rubric of “multi-dimensional continued fractions.” As continued fractions can be…

## On the (non)existence of degenerate phase-shift localised solution in KG (and dNLS) nonlocal lattices – Simone Paleari (Università degli Studi di Milano)

We study the existence of, low amplitude, phase-shift multibreathers for small values of the linear coupling in Klein-Gordon chains with interactions beyond the classical nearest-neighbor (NN) ones. In the proper parameter regimes,…

## On the statistics of extremes for dynamical systems – Mark Holland (University of Exeter)

The study of successive maxima (or minima) for stochastic processes is called Extreme Value Theory. It is extensively used in risk analysis to estimate probabilities of rare events and extremes, e.g. floods; hurricanes; market crashes and general…

## Further developments in pluripotential theory – Azimbay Sadullaev (National University of Uzbekistan)

It is well known that the classical potential theory is based on the class of subharmonic functions and on the Laplace operator. The pluripotential theory, constructed in the 80s of the last century, is based on plurisubharmonic functions and on the…

## Automorphisms of C^2 with an invariant Fatou component biholomorphic to C x C^*. – Jasmin Raissy (Université Paul Sabatier, Toulouse, France)

I will present the construction of a family of automorphisms of C^2having an invariant, non-recurrent Fatou component biholomorphic to C xC* and which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the…

## Non-tangential convergence (and applications to holomorphic dynamics) – Filippo Bracci (Università di Roma Tor Vergata)

The notion of non-tangential convergence is one of the basic concept of complex geoemtry in one and several variables. It is known that univalent maps from the disc into the complex plane admit non-tangential limit almost everywhere on the boundary…

## On the fractal geometry of the Lagrange and Markov spectra. – Carlos Matheus (Paris XIII)

After the remarkable works of Markov in 1879 and 1880, the Lagrange and Markov spectra (coding arithmetic properties of irrational numbers and indefinite binary quadratic forms) were studied by several authors (including Perron, Hall, Freiman,…

## On mixing rates for time-changes of Heisenberg nilflows – Giovanni Forni (University of Maryland)

We construct Bufetov functionals for nilpotent flows on (compact) Heisenberg nilmanifolds. Such functionals were first constructed by Bufetov for Interval Exchange Transformations and Translation flows, and later for horocycle flows by Bufetov and…

## Non-stationary substitutive dynamics and Pisot cocyles – Milton Minervino (Aix-Marseille Université)

We work with shift spaces defined by infinite sequences of simple combinatorial rules called substitutions. To such a system we associate a renormalization cocycle, intimately related with a multidimensional continued fraction algorithm. Under…