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Computer Generated Images for Quadratic Rational Maps with a Periodic Critical Point
rational map complex dynamics plane curve singularities geometric
2010/12/8
We describe an algorithm for distinguishing hyperbolic compo-nents in the parameter space of quadratic rational maps with a periodic critical point. We then illustrate computer images of the hyperboli...
Intermediate asymptotics for critical and supercritical aggregation equations and Patlak-Keller-Segel models
critical supercritical aggregation equations Patlak-Keller-Segel models
2010/12/15
We examine the long-term asymptotic behavior of dissipating solutions to aggregation equations
and Patlak-Keller-Segel models with degenerate power-law and linear diffusion. The purpose
of this work...
Critical Magnetic Number in the MHD Rayleigh-Taylor instability
Rayleigh-Taylor instability MHD free boundary problem critical number
2010/12/14
We reformulate in Lagrangian coordinates the two-phase free boundary problem for the equations of Magnetohydrodynamics in a infinite slab, which is incompressible, vis-cous and of zero resistivity, as...