89 citations · 282 across the 34 of their papers we have counts for
34 papers
Brjuno-Like Functions for nonlinear expanding maps: Fractional Derivatives and Regularity Dichotomies
Stefano Marmi, Daniel Smania
Cohomological equations appear frequently in dynamical systems. One of the most classical examples is the Livšic equation The existence and regulari…
Discontinuous observables as an obstruction for small essential spectral radius
Oliver Butterley, Daniel Smania
We show that for a very wide class of Banach spaces of functions on [0,1] there are intrinsic lower bounds for the essential spectral radius of the transfer operator associated to…
Birkhoff sums as distributions II: Applications to deformations of dynamical systems
Clodoaldo Grotta-Ragazzo, Daniel Smania
Often topological classes of one-dimensional dynamical systems are finite codimension smooth manifolds. We describe a method to prove this sort of statement that we believe can be…
Birkhoff sums as distributions I: Regularity
Clodoaldo Grotta-Ragazzo, Daniel Smania
We study Birkhoff sums as distributions. We obtain regularity results on such distributions for various dynamical systems with hyperbolicity, as hyperbolic linear maps on the torus…
Fractional susceptibility functions for the quadratic family: Misiurewicz-Thurston parameters
Viviane Baladi, Daniel Smania
For the quadratic family, we define the two-variable ( and ) fractional susceptibility function associated to a C^1 observable at a stochastic map. We also define an approxim…
Complex a priori bounds for multicritical circle maps with bounded type rotation number
Gabriela Estevez, Daniel Smania, Michael Yampolsky
In this paper we study homeomorphisms of the circle with several critical points and bounded type rotation number. We prove complex a priori bounds for these maps. As an applicatio…