Piotr Kalita

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20232025

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math.DS2025

$C^{1}$ invariant, stable and inertial manifolds for non-autonomous dynamical systems

Radosław Czaja, Piotr Kalita, Alexandre N. Oliveira-Sousa

We use the version of the Lyapunov--Perron method operating on individual solutions to investigate the existence of invariant manifolds for non-autonomous dynamical systems, focusi…

math.DS2024

Stability of phase portrait for a gradient ODE with memory

Piotr Kalita, Piotr Zgliczyński

We consider the problem governed by the gradient ODE $x^{'} = \nabla F (x)$ in $R^{d}$ on which we assume that it has a finite number of hyperbolic equilibria whose stable and uns…

math.DS2023

Pitchfork bifurcation and heteroclinic connections in the Kuramoto--Sivashinsky PDE

Jacek Kubica, Piotr Zgliczyński, Piotr Kalita

We present a method for the complete analysis of the dynamics of dissipative Partial Differential Equations (PDEs) undergoing a pitchfork bifurcation. We apply our technique to the…

C1 invariant, stable and inertial manifolds for non-autonomous dynamical systems

Stability of phase portrait for a gradient ODE with memory

Pitchfork bifurcation and heteroclinic connections in the Kuramoto--Sivashinsky PDE

$C^{1}$ invariant, stable and inertial manifolds for non-autonomous dynamical systems