Add to ORKGInternational audienceWe investigate in this work a local version of the theory of fractal strings and associated geometric zeta functions. Such a generalization allows to describe the asymptotic behaviour of a "fractal" set in the neighborhood of any of its points. We give basic properties and several examples illustrating the possible range of situations concerning in particular the evolution of the local complex dimensions along the set and the relation between local and global zeta functions
Abstract. We discuss a number of techniques for determining the Minkowski dimension of bounded subse...
Offers a study of the vibrations of fractal strings, that is, one-dimensional drums with fractal bou...
Fractal geometry is usually studied in the context of bounded sets. In this setting,\ud various prop...
International audienceWe investigate in this work a local version of the theory of fractal strings a...
International audienceWe investigate in this work a local version of the theory of fractal strings a...
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional...
For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one...
In this paper a string is a sequence of positive non-increasing real numbers which sums to one. For ...
In this paper a string is a sequence of positive non-increasing real numbers which sums to one. For ...
International audienceIn this paper, we generalize the zeta function for a fractal string (as in [18...
The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) o...
International audienceIn this paper, we generalize the zeta function for a fractal string (as in [18...
Abstract. For a Borel measure on the unit interval and a se-quence of scales that tend to zero, we d...
Fractal zeta functions associated to bounded subsets of Euclidean spaces relate the geometry of a se...
In the first chapter we define and look at examples of self-similar sets and some of\ud their proper...
Abstract. We discuss a number of techniques for determining the Minkowski dimension of bounded subse...
Offers a study of the vibrations of fractal strings, that is, one-dimensional drums with fractal bou...
Fractal geometry is usually studied in the context of bounded sets. In this setting,\ud various prop...
International audienceWe investigate in this work a local version of the theory of fractal strings a...
International audienceWe investigate in this work a local version of the theory of fractal strings a...
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional...
For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one...
In this paper a string is a sequence of positive non-increasing real numbers which sums to one. For ...
In this paper a string is a sequence of positive non-increasing real numbers which sums to one. For ...
International audienceIn this paper, we generalize the zeta function for a fractal string (as in [18...
The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) o...
International audienceIn this paper, we generalize the zeta function for a fractal string (as in [18...
Abstract. For a Borel measure on the unit interval and a se-quence of scales that tend to zero, we d...
Fractal zeta functions associated to bounded subsets of Euclidean spaces relate the geometry of a se...
In the first chapter we define and look at examples of self-similar sets and some of\ud their proper...
Abstract. We discuss a number of techniques for determining the Minkowski dimension of bounded subse...
Offers a study of the vibrations of fractal strings, that is, one-dimensional drums with fractal bou...
Fractal geometry is usually studied in the context of bounded sets. In this setting,\ud various prop...