Nonlinear aspects of astrobiological research

Several aspects of mathematical astrobiology are discussed. It is argued that around the time of the origin of life the handedness of biomolecules must have established itself through an instability. Possible pathways of producing a certain handedness include mechanisms involving either autocatalysis or, alternatively, epimerization as governing effects. Concepts for establishing hereditary information are discussed in terms of the theory of hypercycles. Instabilities toward parasites and possible remedies by invoking spatial extent are reviewed. Finally, some effects of early life are discussed that contributed to modifying and regulating atmosphere and climate of the Earth, and that could have contributed to the highly oxidized state of its crust.