Author

W. Szumiński

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Preprint Sep 2026

Dynamics, periodic orbits and $C^1$ non-integrability of the ABC flow

We study the Arnold-Beltrami-Childress (ABC) flow in perturbative regimes near its three elementary integrable coordinate axes. Starting from a degenerate family of periodic streamlines of the limiting integrable system, we use first-order averaging to prove the existence of two isolated periodic solutions of the pertu...

Wojciech Szumiński, Jaume Llibre · 0 citations

Preprint Sep 2026

Trigonometric Nos\'e--Hoover oscillator: chaos, periodic orbits and integrability

We introduce a trigonometric version of the Nos\'e-Hoover oscillator in which the quadratic mechanical terms and unbounded thermostat coupling are replaced by bounded trigonometric functions. This formulation replaces the harmonic potential by a pendulum-type potential and confines the thermostat interaction to a bound...

Wojciech Szumiński, Jaume Llibre · 0 citations

Preprint Aug 2026

Dynamics and non-integrability of the Swinging Atwood Machine with a massive string: chaos, periodic orbits and resonance structures

Building upon our previous studies on nonlinear variable-length pendulum systems, we investigate the Swinging Atwood Machine with a massive string. In contrast to the classical model, string inertia introduces a configuration-dependent moment of inertia, leading to a modified Hamiltonian structure and substantially ric...

W. Szumiński, Jakub Bembenek · 0 citations