MATHEMATICA BOHEMICA, Vol. 129, No. 2, pp. 129-140 (2004)

Dynamics of dianalytic transformations
of Klein surfaces

Ilie Barza, Dorin Ghisa

Ilie Barza, Karlstad University, Dpt. of Engineering Sciences, Physics and Mathematics, S-651 88-Karlstad, Sweden, e-mail:; Dorin Ghisa, York University, Glendon College, Department of Mathematics, 2275-Bayview Avenue, Toronto, Canada, M4N 3M6, e-mail:

Abstract: This paper is an introduction to dynamics of dianalytic self-maps of nonorientable Klein surfaces. The main theorem asserts that dianalytic dynamics on Klein surfaces can be canonically reduced to dynamics of some classes of analytic self-maps on their orientable double covers. A complete list of those maps is given in the case where the respective Klein surfaces are the real projective plane, the pointed real projective plane and the Klein bottle.

Keywords: nonorientable Klein surface, dianalytic self-map, Julia set, Fatou set, dianalytic dynamics

Classification (MSC2000): 30F50, 37F50

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