5 papers
Faithfulness and fractal (quasi-)equivalence principles for Perron, Engel, and Pierce expansions
Mykola Moroz
We establish several unifying principles that clarify the fractal properties of classical number expansions, which are generalized by the Perron expansions. In particular, we prove…
Hölder exponents and fractal structure of level sets of self-affine functions associated with the -representation of numbers
Volodymyr Yelahin, Mykola Moroz
We investigate a class of locally complicated self-affine functions defined via the -representation of real numbers. In particular, we compute local Hölder exponents at point…
A counterexample to the Karvatskyi--Pratsiovytyi conjecture concerning the achievement set of an intermediate series
Mykola Moroz
We found a counterexample to the conjecture of Karvatskyi and Pratsiovytyi concerning the topological type of the achievement set of an intermediate series (Proceedings of the Inte…
The convergence of sequences in terms of positive and alternating Perron expansions
Mykola Moroz
We consider conditions for the convergence of sequences in terms of positive and alternating Perron expansions (-representation and -representation). These conditions are c…
Representations of Real Numbers by Alternating Perron Series and Their Geometry
Mykola Moroz
We consider the representation of real numbers by alternating Perron series (-representation), which is a generalization of representations of real numbers by Ostrogradsky-Sie…