We prove that any two real-analytic critical circle maps with cubic critical point and the same irrational rotation number of bounded type are C 1+α conjugate for some α > 0.
OBJECTIVE To study the value of epicardial mapping through the coronary venous system in patients with sustained ventricular tachycardia. DESIGN 20 consecutive patients with sustained ventricular tachycardia who were candidates for radiofrequency ablation. SETTING Electrophysiological laboratory. INTERVENTIONS Coronary venous angiography was performed… (More)
The existence of smooth families of Lorenz maps exhibiting all possible dynamical behavior is established and the structure of the parameter space of these families is described.
In this paper we extend M. Lyubich's recent results on the global hyper-bolicity of renormalization of quadratic-like germs to the space of C r unimodal maps with quadratic critical point. We show that in this space the bounded-type limit sets of the renormalization operator have an invariant hyperbolic structure provided r ≥ 2 + α with α close to one. As… (More)
It will be shown that the smooth conjugacy class of an S−unimodal map which does not have a periodic attractor neither a Cantor attractor is determined by the multipliers of the periodic orbits. This generalizes a result by M.Shub and D.Sullivan for smooth expanding maps of the circle.
n → R p is a map. We say that f is differentiable at x if there exists a linear transformation L : R n → R p such that, f (x + h) = f (x) + L(h) + r(x, h), where ∥r(x,h)∥ ∥h∥ → 0 when h → 0. If such L exists, it is unique. In this case, we call L the derivative of f at point x. If f is differentiable at any point of U , then df : U ⊂ R n → L(R n , R p) ≃ R… (More)
Alejandro Kocsard received financial support from CNPq and FAPERJ (Brazil). Abstract Given a smooth vector field X on a closed orientable d-manifold M, many questions about the dynamics of its induced flow can be studied analyzing the following cohomological equation: L X u = ξ, where ξ is a given real function on M, u : M → R is the solution that we look… (More)
Here we review some recent results that give a rather complete description of the dynamics of almost all mappings in real analytic families of unimodal maps 1. THE RESULTS We will review here some recent results on the rich dynamics and bi-furcation structure in one dimensional families of real analytic unimodal maps. The domain of our maps will be… (More)
We prove that two C r critical circle maps with the same rotation number of bounded type are C 1+α conjugate for some α > 0 provided their successive renormalizations converge together at an exponential rate in the C 0 sense. The number α depends only on the rate of convergence. We also give examples of C ∞ critical circle maps with the same rotation number… (More)