Structural stability and hyperbolicity violation in high-dimensional dynamical systems
| العنوان: | Structural stability and hyperbolicity violation in high-dimensional dynamical systems |
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| المؤلفون: | Julien Clinton Sprott, David J. Albers |
| المصدر: | Nonlinearity. 19:1801-1847 |
| بيانات النشر: | IOP Publishing, 2006. |
| سنة النشر: | 2006 |
| مصطلحات موضوعية: | Mathematics::Dynamical Systems, Dynamical systems theory, Applied Mathematics, 010102 general mathematics, General Physics and Astronomy, Statistical and Nonlinear Physics, Observable, Monotonic function, Lyapunov exponent, Parameter space, Topological space, 16. Peace & justice, Topology, 01 natural sciences, 010305 fluids & plasmas, symbols.namesake, Structural stability, 0103 physical sciences, symbols, Dissipative system, Statistical physics, 0101 mathematics, Mathematical Physics, Mathematics |
| الوصف: | This report investigates the dynamical stability conjectures of Palis and Smale and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical system is increased, it is observed that the number of positive Lyapunov exponents increases monotonically, the Lyapunov exponents tend towards continuous change with respect to parameter variation, the number of observable periodic windows decreases (at least below numerical precision) and a subset of parameter space exists such that topological change is very common with small parameter perturbation. However, this seemingly inevitable topological variation is never catastrophic (the dynamic type is preserved) if the dimension of the system is high enough. |
| تدمد: | 1361-6544 0951-7715 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_________::cf4e43810a171ef8b2d7559bd79eb7cbTest https://doi.org/10.1088/0951-7715/19/8/005Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi...........cf4e43810a171ef8b2d7559bd79eb7cb |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 13616544 09517715 |
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