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Marcus Werner Beims

Publications and source records attributed to Marcus Werner Beims.

2 recordsLinked to original sources
arXiv2024

Lyapunov stability under $q$-dilatation and $q$-contraction of coordinates

This study examines the Lyapunov stability under coordinate $q$-contraction and $q$-dilatation in three dynamical systems: the discrete-time dissipative Hénon map, and the conservative, non-integrable, continuous-time Hénon-Heiles and diamagnetic Kepler problems. The stability analysis uses the $q$-deformed Jacobian and $q$-derivative, with trajectory stability assessed for $q > 1$ (dilatation) and $q < 1$ (contraction). Analytical curves in the parameter space mark boundaries of distinct low-periodic motions in the Hénon map. Numerical simulations compute the maximal Lyapunov exponent across the parameter space, in Poincaré surfaces of section, and as a function of total energy in the conservative systems. Simulations show that $q$-contraction ($q$-dilatation) generally decreases (increases) positive Lyapunov exponents relative to the $q = 1$ case, while both transformations tend to increase Lyapunov exponents for regular orbits. Some exceptions to this trend remain unexplained regarding Kolmogorov-Arnold-Moser (KAM) tori stability.

nlin.CD↗
arXiv2009

Dissipation effects in the ratchetlike Fermi acceleration

Ac driven asymmetric pulses can be used to control the Fermi acceleration between three different motions, ${\bf A:}$ the {\it accelerated} mode; ${\bf D:}$ the {\it decelerated} mode and ${\bf H:}$ the {\it hyperaccelerated} mode. In this work we show that dissipation strongly affects the particles velocity, reducing the possibility for an accurate control of the dynamics. The saturation time, where the mean velocity starts to be constant due to dissipation, decays with a power law $\simγ^{-β}$, where $γ$ is the dissipation parameter and $β$ is close to 1. The value of the saturated mean velocity also decays with a power law with exponent $β\sim0.6$ for the case ${\bf H}$, and $β\sim0.3$ for the case ${\bf A}$. In the case ${\bf D}$ this velocity is almost constant for small dissipations.

nlin.CD↗