2 citations · 3 across the 4 of their papers we have counts for
7 papers
Periodic and chaotic dynamics in a map-based neuron model
Frank Llovera Trujillo, Justyna Signerska-Rynkowska, Piotr Bartłomiejczyk
Map-based neuron models are an important tool in modelling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on con…
Gradient versus proper gradient homotopies
Piotr Bartłomiejczyk, Piotr Nowak-Przygodzki
We compare the sets of homotopy classes of gradient and proper gradient vector fields in the plane. Namely, we show that gradient and proper gradient homotopy classifications are e…
Topological degree for equivariant gradient perturbations of an unbounded self-adjoint operator in Hilbert space
Piotr Bartłomiejczyk, Bartosz Kamedulski, Piotr Nowak-Przygodzki
We present a version of the equivariant gradient degree defined for equivariant gradient perturbations of an equivariant unbounded self-adjoint operator with purely discrete spectr…
Degree product formula in the case of a finite group action
Piotr Bartłomiejczyk, Bartosz Kamedulski, Piotr Nowak-Przygodzki
Let be finite-dimensional orthogonal representations of a finite group . The equivariant degree with values in the Burnside ring of has been studied extensively by ma…
Otopy classification of gradient compact perturbations of identity in Hilbert space
Piotr Bartłomiejczyk, Piotr Nowak-Przygodzki
We prove that the inclusion of the space of gradient local maps into the space of all local maps from Hilbert space to itself induces a bijection between the sets of the respective…
The Hopf type theorem for equivariant gradient local maps
Piotr Bartłomiejczyk, Piotr Nowak-Przygodzki
We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite dimensional orthogonal representation of a compact Lie group. We prove t…
The Hopf type theorem for equivariant local maps
Piotr Bartłomiejczyk
We study otopy classes of equivariant local maps and prove the Hopf type theorem for such maps in the case of a real finite dimensional orthogonal representation of a compact Lie g…