Herglotz functions and solutions of the Feigenbaum-Cvitanovic equation: a numerical approach

Alexei Tsygvintsev

Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestrershire, LE 11 3TU, UK

A.Tsygvintsev@lboro.ac.uk

http://www.lboro.ac.uk/departments/ma/staff/at/

Contributed talk

In this talk, we give a new approach to the construction of solutions of the Feigenbaum-Cvitanovic equation whose existence was shown by E. Epstein. Our main tool is the theory of Herglotz functions and the analytic theory of continued fractions.