7 papers
Linear relations modulo meager sets
Marek Balcerzak, Paolo Leonetti
We prove several topological zero-one laws. First, we show that, if a subset of a Banach space has the Baire property, then admits a somewhere dense set of vectors $x \…
Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane
Gonzalo Marcelo RamÃrez-Ãvila, S. Leo Kingston, Marek Balcerzak +3
We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynam…
Electronic Equivalent of a Mechanical Impact Oscillator
Volodymyr Denysenko, Marek Balcerzak, Artur Dabrowski
This paper presents a novel design of an electronic circuit that is equivalent to a mechanical discontinuous impact oscillator exhibiting hard impacts. The governing equations of t…
Master Stability Function for networks of coupled non-smooth oscillators
Volodymyr Denysenko, Marek Balcerzak, Artur Dabrowski
This paper describes extension of the Master Stability Function for arrays of non-smooth oscillators. This extension is based on the previously introduced Jacobi matrix estimation…
Topological complexity of ideal limit points
Marek Balcerzak, Szymon Glab, Paolo Leonetti
Given an ideal on the nonnegative integers and a Polish space , let be the family of subsets such that is the se…
Point-set games and functions with the hereditary small oscillation property
Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca
Given a metric space , we consider certain families of functions having the hereditary oscillation property HSOP and the hereditary continuous restriction pro…