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Let f be a transcendental entire function and let A(f) denote the set of points that escape to infinity ‘as fast as possible’ under iteration. By writing A(f) as a countable union of closed sets, call...
Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
Singular Points Eikonal Partial Differential Equations
2010/11/1
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equatio...