| 概要 | We will present recent work on two intensely studied
problems in dynamical systems. The first deals with
the discrete quadratic map; here the long-standing
question concerns the regions of stability when varying
the parameter of the map. The second topic concerns
Hilbert's 16th problem, which asks for the possible
number (and configuration) of limit cycles for planar
polynomial vector fields.
Both problems have been thoroughly studied for more
than a century, and with a formidable variation of
techniques. We will show how validated numerics can
contribute to gaining further insight into these
problems. This work is joint with Daniel Wilczak
and Tomas Johnson, respectively.
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