Report
Lyapunov stability under $q$-dilatation and $q$-contraction of coordinates
| العنوان: | Lyapunov stability under $q$-dilatation and $q$-contraction of coordinates |
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| المؤلفون: | de Oliveira, Tulio Meneghelli, Wiggers, Vinicius, Scafi, Eduardo, Zanin, Silvio, Manchein, Cesar, Beims, Marcus Werner |
| سنة النشر: | 2024 |
| المجموعة: | Nonlinear Sciences |
| مصطلحات موضوعية: | Nonlinear Sciences - Chaotic Dynamics, 34C28, 37D45 |
| الوصف: | This study examines the Lyapunov stability under coordinate $q$-contraction and $q$-dilatation in three dynamical systems: the discrete-time dissipative H\'enon map, and the conservative, non-integrable, continuous-time H\'enon-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 H\'enon map. Numerical simulations compute the maximal Lyapunov exponent across the parameter space, in Poincar\'e 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. Comment: 15 pages, 8 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2411.18691 |
| رقم الانضمام: | edsarx.2411.18691 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |