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Irregular solutions of the Feigenbaum functional equation

Bartłomiejczyk L.

Demonstratio Mathematica

2005

Vol. 38, nr 1

135--141

We describe the structure of orbits generated by two commuting bijections and using this description we construct irregular solutions of the Feigenbaum functional equation. The graph of such a solution almost cover the plane in the sense of measure and topology.

Solutions with big graph of the equation of invariant curves

Bartłomiejczyk L.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 3

309-317

We consider the functional equation of invariant curves [phi(f(x, phi(x))) = g(x, phi(x))] and we look for its solution which has a big graph. Such a graph is big from the point of view of topology and measure theory.