We prove the existence of C- (but not Cr+i-) regular central Cantor sets with zero Lebesgue measure such that their self arithmetic difference is a Cantor set with positive Lebesgue measure. This is motivated by a conjecture in the field of bifurcations of dynamical systems posed by Jacob Palis. 1
Furstenberg, using topological dynamics, defined the notion of a central set of positive integers, a...
ABSTRACT. This breif note defines the idea of a “very fat ” Cantor set, and breifly exam-ines the me...
We show that under natural technical conditions, the sum of a $C^2$ dynamically defined Cantor set w...
Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor se...
Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor se...
Abstract. An example of a regular Cantor set whose self-difference set is a Cantor set with a positi...
AbstractIn this paper we consider a family of random Cantor sets on the line. We give some sufficien...
We define a self-similar set as the (unique) invariant set of an iterated function system of certain...
International audienceIn this paper we establish a new connection between central sets and the stron...
International audienceIn this paper we establish a new connection between central sets and the stron...
Many examples exist of one-dimensional systems that are topologically conjugate to the shift operato...
AbstractIn this paper we consider a family of random Cantor sets on the line. We give some sufficien...
AbstractIt is shown that the arithmetic sum of middle-α Cantor sets typically has positive Lebesgue ...
The middle-third Cantor set is one of the most fundamental examples of self-similar fractal sets int...
The middle-third Cantor set is one of the most fundamental examples of self-similar fractal sets int...
Furstenberg, using topological dynamics, defined the notion of a central set of positive integers, a...
ABSTRACT. This breif note defines the idea of a “very fat ” Cantor set, and breifly exam-ines the me...
We show that under natural technical conditions, the sum of a $C^2$ dynamically defined Cantor set w...
Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor se...
Every central Cantor set of positive Lebesgue measure is the arithmetic sum of two central Cantor se...
Abstract. An example of a regular Cantor set whose self-difference set is a Cantor set with a positi...
AbstractIn this paper we consider a family of random Cantor sets on the line. We give some sufficien...
We define a self-similar set as the (unique) invariant set of an iterated function system of certain...
International audienceIn this paper we establish a new connection between central sets and the stron...
International audienceIn this paper we establish a new connection between central sets and the stron...
Many examples exist of one-dimensional systems that are topologically conjugate to the shift operato...
AbstractIn this paper we consider a family of random Cantor sets on the line. We give some sufficien...
AbstractIt is shown that the arithmetic sum of middle-α Cantor sets typically has positive Lebesgue ...
The middle-third Cantor set is one of the most fundamental examples of self-similar fractal sets int...
The middle-third Cantor set is one of the most fundamental examples of self-similar fractal sets int...
Furstenberg, using topological dynamics, defined the notion of a central set of positive integers, a...
ABSTRACT. This breif note defines the idea of a “very fat ” Cantor set, and breifly exam-ines the me...
We show that under natural technical conditions, the sum of a $C^2$ dynamically defined Cantor set w...
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