25 citations · 78 across the 8 of their papers we have counts for
11 papers
Trigonometric Nosé--Hoover oscillator: chaos, periodic orbits and integrability
Wojciech Szumiński, Jaume Llibre
We introduce a trigonometric version of the Nosé-Hoover oscillator in which the quadratic mechanical terms and unbounded thermostat coupling are replaced by bounded trigonometric f…
Dynamics, periodic orbits and non-integrability of the ABC flow
Wojciech Szumiński, Jaume Llibre
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 stream…
Zero-Hopf bifurcation, periodic orbits and non-integrability of the classical Rössler system
Jaume Llibre, Wojciech Szumiński
We investigate the zero-Hopf bifurcation and the local -non-integrability of the original Rössler system. First, we characterize the unique zero-Hopf equilibrium of the syst…
Dynamics and non-integrability of the Swinging Atwood Machine with a massive string: chaos, periodic orbits and resonance structures
Wojciech Szumiński, Jakub Bembenek
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 mod…
Integrability of non-homogeneous Hamiltonian systems with gyroscopic coupling
Wojciech Szumiński, Andrzej J. Maciejewski
We study the integrability of a two-dimensional Hamiltonian system with a gyroscopic term and a non-homogeneous potential composed of two homogeneous components of different degree…
Dynamics and non-integrability of the variable-length double pendulum: exploring chaos and periodicity via the Lyapunov refined maps
Wojciech Szumiński, Tomasz Kapitaniak
This paper extends our previous work~(Szumiński and Maciejewski, 2024), where we explored the dynamics and integrability of the double-spring pendulum. Here, we investigate the var…
Dynamics and non-integrability of the double spring pendulum
Wojciech Szumiński, Andrzej J. Maciejewski
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Ha…
A new model of variable-length coupled pendulums: from hyperchaos to superintegrability
Wojciech Szumiński
This paper studies the dynamics and integrability of a variable-length coupled pendulum system. The complexity of the model is presented by joining various numerical methods, such…
Destructive relativity
Maria Przybylska, Wojciech Szumiński, Andrzej J. Maciejewski
Relativistic Hamiltonian equations describing a motion of a point mass in an arbitrary homogeneous potential are considered. For the first time, the necessary integrability conditi…
Non-integrability of the semiclassical Jaynes--Cummings models without the rotating-wave approximation
Andrzej J. Maciejewski, Wojciech Szumiński
Two versions of the semi-classical Jaynes--Cummings model without the rotating wave approximation are investigated. It is shown that for a non-zero value of the coupling constant t…
Non-integrability of the dumbbell and point mass problem
Andrzej J. Maciejewski, Maria Przybylska, Leon Simpson +1
This paper discusses a constrained gravitational three-body problem with two of the point masses separated by a massless inflexible rod to form a dumbbell. The non-integrability of…