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Jumping property of Lyapunov values. (English) Zbl 0847.34032

For distinguishing between center and focus in a planar vector field described by (1) \(\dot x=- y+ f(x, y)\), \(\dot y= x+ g(x, y)\), one has to calculate the Lyapunov values of (1). A convenient way to do this is to change (1) to its equivalent complex form (2) \(\dot z= iz+ F(z, \overline {z})\). In [Random Comput. Dyn. 2, 261-277 (1994; Zbl 0829.34023)] the authors introduced the notion of \(k\)th standard Lyapunov value \(L_k (F)\). In this paper they list (without proofs) certain properties of the values \(L_k (F)\).
Reviewer: W.Müller (Berlin)

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Citations:

Zbl 0829.34023
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