1,723,273 research outputs found
Critical functions for complex analytic maps
No full textCritical functions measure the width of the domain of stability around a given fixed point or an invariant circle for complex analytic and area-preserving maps. The author discusses their dependence on the rotation number of the invariant curves and proposes some new methods to determine them based on the existence of critical points and on some properties of quasiconformal maps. By means of the majorant series method some rigorous estimates are given for complex area-preserving maps like the semistandard map and the modulated singular map. In particular, the author makes use of the Brjuno function to interpolate critical maps and proves that the convergence of the Brjuno function is a necessary and sufficient condition for the existence of an analytic invariant curve of a given rotation number. The author also discusses the optimality of the rigorous bounds obtained
Cohomological equations for linear involutions
No full textIn the current note, we extend results by Marmi, Moussa and Yoccoz about cohomological equations for interval exchange transformations to irreducible linear involutions
A Method for Accurate Stability Bounds in a Small Denominator Problem
No full textThe author considers the problem of obtaining realistic lower bounds for the Siegel radius. Recent advances of the analysis of Siegel disks allows one to give a very accurate numerical algorithm based on rigorous results. He finds that for non-quadratic polynomial maps the maximal Siegel radius might correspond to rotation numbers different from the golden mean
Gio' Pomodoro la figlia del sole ; un percorso espositivo per Forte dei Marmi, 19 giugno - 27 luglio 2004
No full textThe Yoccoz-Birkeland livestock population model coupled with random price dynamics
No full textWe study a random version of the population-market model proposed by Arlot,
Marmi and Papini in Arlot et al. (2019). The latter model is based on the
Yoccoz-Birkeland integral equation and describes a time evolution of livestock
commodities prices which exhibits endogenous deterministic stochastic
behaviour. We introduce a stochastic component inspired from the Black-Scholes
market model into the price equation and we prove the existence of a random
attractor and of a random invariant measure. We compute numerically the fractal
dimension and the entropy of the random attractor and we show its convergence
to the deterministic one as the volatility in the market equation tends to
zero. We also investigate in detail the dependence of the attractor on the
choice of the time-discretization parameter. We implement several statistical
distances to quantify the similarity between the attractors of the discretized
systems and the original one. In particular, following a work by Cuturi (2013),
we use the Sinkhorn distance. This is a discrete and penalized version of the
Optimal Transport Distance between two measures, given a transport cost matrix
Marmi imitati e marmi reimpiegati in Ostia Tardoantica
No full textEsame analitico dei materiali lapidei certamente reimpiegati nel Mitreo dei marmi colorati. Studio delle pitture imitanti i marmi nel Mtreo dei marmi colorati di Ostia antica
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