Diophantine classes, dimension and Denjoy maps
Dirichlet forms on quotients of shift spaces
We define thin equivalence relations ∼ on shift spaces and derive Dirichlet forms on the quotient space in terms of the nearest neighbour averaging operator. We identify the associated Laplace operator. The conditions are applied to some non-self-similar extensions of the Sierpiński gasket.
Discrepancies of point sequences on the Sierpiński carpet
Discrete self-similar multifractals with examples from algebraic number theory
Distribution of digits in integers: fractal dimensions and zeta functions
Domains of Dirichlet forms and effective resistance estimates on p.c.f. fractals
We consider post-critically finite self-similar fractals with regular harmonic structures. We first obtain effective resistance estimates in terms of the Euclidean metric, which in particular imply the embedding theorem for the domains of the Dirichlet forms associated with the harmonic structures. We then characterize the domains of the Dirichlet forms.
Dynamical boundary of a self-similar set
Given a self-similar set E generated by a finite system Ψ of contracting similitudes of a complete metric space X we analyze a separation condition for Ψ, which is obtained if, in the open set condition, the open subset of X is replaced with an open set in the topology of E as a metric subspace of X. We prove that such a condition, which we call the restricted open set condition, is equivalent to the strong open set condition. Using the dynamical properties of the forward shift, we find a canonical...
Dynamics of certain nonconformal degree-two maps of the plane.
Dynamics of finite-multivalued transformations.
Eigenvalue estimates for a class of operators related to self-similar measures
Erratum to “Geometric rigidity of invariant measures” (J. Eur. Math. Soc. 14, 1539–1563 (2012))
Estimations de la dimension inférieure et de la dimension supérieure des mesures
Existence and properties of -sets.
Existence and uniqueness of diffusions on finitely ramified self-similar fractals
Existence et régularité höldérienne des fonctions de bosses
We discuss the almost sure existence of random functions that can be written as sums of elementary pulses. We then estimate their uniform Hölder regularity by applying some results on coverings by random intervals.
Extremely non-normal continued fractions
Fourier Asymptotics of Statistically Self-Similar Measures.
Fractal Differential Equations on the Sierpinski Gasket.
Fractal dimension of sets induced by bases of imaginary quadratic fields
Fractal geometry as design aid.