An earthquake version of the Jackson-Zygmund theorem.
Complex a priori bounds revisited
Computing explicitly topological sequence entropy: the unimodal case
Let denote the family of continuous maps from an interval into itself such that (1) ; (2) they consist of two monotone pieces; and (3) they have periodic points of periods exactly all powers of . The main aim of this paper is to compute explicitly the topological sequence entropy of any map respect to the sequence .
Different types of scaling in the dynamics of period-doubling maps under external periodic driving.
Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture.
Hyperbolicity of renormalization of critical circle maps
Intertwined mappings
On the topological dynamics and phase-locking renormalization of Lorenz-like maps
The aim of this paper is twofold. First we give a characterization of the set of kneading invariants for the class of Lorenz–like maps considered as a map of the circle of degree one with one discontinuity. In a second step we will consider the subclass of the Lorenz– like maps generated by the class of Lorenz maps in the interval. For this class of maps we give a characterization of the set of renormalizable maps with rotation interval degenerate to a rational number, that is, of phase–locking...
Period doubling, entropy, and renormalization
We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.
Regularity of conjugacies between critical circle maps: an experimental study.
Retracts, fixed point index and differential equations.
Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.
Substitutions and 1/2-discrepancy of nθ + x
Sulla stabilità di un punto fisso per funzioni di variabili complesse. Problema del Centro di Schröder-Siegel
Viene considerato il problema della stabilità di un punto fisso per un germe di diffeomorfismo di più variabili complesse cercando un coniugio con la sua parte lineare: Problema del centro di Schröder-Siegel. Dopo aver formulato il problema e ricordato i principali risultati nel caso di diffeomorfismi olomorfi, mostriamo come estendere il problema ad alcune situazioni non olomorfe, in particolare ci interesseremo al caso di germi Gevrey. Concluderemo con un'applicazione rivolta a mostrare la stabilità...
The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
Thurston unbounded earthquake maps.
Topological and measurable dynamics of Lorenz maps [Book]
Universality and scaling in networks of period-doubling maps with a pacemaker.
Wavelet-based quantum field theory.