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Complicated dynamics in nonautonomous ODEs. (English) Zbl 1068.34043
The authors apply a topological method for detecting complicated dynamics in some processes generated by nonautonomous ordinary differential equations. To this end, some admissible proper sets are constructed and some topological invariants of these sets are also proved. It is shown that the equation \(\dot{z}=(1+(\cos(t^2)+2)e^{I\phi t}| z| ^2)\bar{z}\) fulfils the assumptions of the main result for sufficiently small \(\phi>0\) and therefore, this equation exhibits complicated dynamical behavior.

MSC:
34C28 Complex behavior and chaotic systems of ordinary differential equations
37B55 Topological dynamics of nonautonomous systems
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