The Brjuno functions and their regularity properties
From MaRDI portal
Publication:1363160
DOI10.1007/s002200050110zbMath0947.30018OpenAlexW1991371085MaRDI QIDQ1363160
Pierre Moussa, Jean-Christophe Yoccoz, Stefano Marmi
Publication date: 18 August 1997
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s002200050110
Topological dynamics (37B99) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Continued fractions (11A55) Continued fractions; complex-analytic aspects (30B70) Dynamical systems over complex numbers (37F99)
Related Items (50)
Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics ⋮ Simultaneous linearization of germs of commuting holomorphic diffeomorphisms ⋮ Analytic solutions of an iterative functional differential equations near regular points ⋮ A convergence criterion for the unstable manifolds of the MacKay approximate renormalisation ⋮ Existence of analytic invariant curves for a complex planar mapping near resonance ⋮ Renormalization-group analysis for the transition to chaos in Hamiltonian systems ⋮ Analytic linearization of a generalization of the semi-standard map: radius of convergence and Brjuno sum ⋮ Local invertible analytic solutions for an iterative differential equation related to a discrete derivatives sequence ⋮ A normal form theorem for Brjuno skew systems through renormalization ⋮ Generalized Brjuno functions associated to \(\alpha \)-continued fractions ⋮ Response solutions for strongly dissipative quasi-periodically forced systems with arbitrary nonlinearities and frequencies ⋮ Analytic solutions for a class of differential equations with delays depending on state ⋮ Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin ⋮ Arithmetic geometric model for the renormalisation of irrationally indifferent attractors ⋮ A proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type ⋮ Analytic solutions for a functional differential equation related to a traffic flow model ⋮ Regularity properties of \(k\)-Brjuno and Wilton functions ⋮ On the Legendre constant of \(\alpha \)-continued fractions ⋮ Matching for a family of infinite measure continued fraction transformations ⋮ Small divisors problem in dynamical systems and analytic invariant curves for an iterative equation related to a rational difference equation ⋮ Book review of: M. Braverman and M. Yampolsky, Computability of Julia sets ⋮ On the minimum of the Brjuno function ⋮ New Exponents for Pointwise Singularity Classification ⋮ Estimates of sums related to the Nyman-Beurling criterion for the Riemann hypothesis ⋮ Complex Brjuno functions ⋮ On a Category of Cotangent Sums Related to the Nyman-Beurling Criterion for the Riemann Hypothesis ⋮ On the relationship between the Bruno function and the breakdown of invariant tori ⋮ Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann hypothesis ⋮ Multifractal analysis of the Brjuno function ⋮ The 1/2-Complex Bruno Function and the Yoccoz Function: A Numerical Study of the Marmi-Moussa-Yoccoz Conjecture ⋮ Differentiability of arithmetic Fourier series arising from Eisenstein series ⋮ Small divisors problem in dynamical systems and analytic solutions of the Shabat equation ⋮ Existence of analytic solutions of an iterative functional equation ⋮ Exponentially long time stability for non-linearizable analytic germs of \(({\mathbb C}^n,0)\).. ⋮ On computational complexity of Siegel Julia sets ⋮ Local analytic solutions of a functional differential equation \(\alpha z+\beta x'(z)= x(az+bx(z))\) ⋮ Analytic invariant curves for an iterative equation related to Ricker-type second-order equation ⋮ Non-computable Julia sets ⋮ Analytic invariant curves for an iterative equation related to dissipative standard map ⋮ Analytic solutions of an iterative differential equation under Brjuno condition ⋮ Analytic invariant curves for an iterative equation related to Pielou's equation ⋮ Constructing locally connected non-computable Julia sets ⋮ Linearization of analytic and non-analytic germs of diffeomorphisms of $({\mathbb C},0)$ ⋮ Continued fractions and Brjuno functions ⋮ Non-computable impressions of computable external rays of quadratic polynomials ⋮ Scaling properties for the radius of convergence of a Lindstedt series: The standard map ⋮ Analytic invariant curves for an iterative equation related to mosquito model ⋮ Analytic solutions of a second-order functional differential equation ⋮ The order of magnitude for moments for certain cotangent sums ⋮ Computable Geometric Complex Analysis and Complex Dynamics
This page was built for publication: The Brjuno functions and their regularity properties
