Dynamic stability of high-dimensional dynamical systems
نویسندگان
چکیده
The dynamical stability conjectures of Palis and Smale, and Pugh and Shub are investigated from the stand-point of numerical observation, and a new stability conjecture is proposed. As the dimension of a dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically, the number of observable periodic windows decreases, and there is a subset of parameter space 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 sufficiently high.
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