Local behavior of planar analytic vector fields via integrability (Q641580)
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scientific article; zbMATH DE number 5962606
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| English | Local behavior of planar analytic vector fields via integrability |
scientific article; zbMATH DE number 5962606 |
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Local behavior of planar analytic vector fields via integrability (English)
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24 October 2011
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A method to study the behaviour of trajectories near a singular point in planar analytic systems of the form \[ \dot{x}=P(x,y),\;\;\dot{y}=Q(x,y) \] is presented. It can be applied provided the system has a first integral which is a quotient of analytic functions. In particular, the method can be applied to vector fields with a rational first integral. Examples illustrate the method.
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planar analytic vector field
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generalized rational first integral
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blow-up
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