Onedimensional maps and Poincaré metric
Abstract
Invertible compositions of onedimensional maps are studied which are assumed to include maps with nonpositive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show that the joint distortion of the composition is bounded. On the other hand, if all maps with possibly nonnegative Schwarzian derivative are almost linearfractional and their nonlinearities tend to cancel leaving only a small total, then they can all be replaced with affine maps with the same domains and images and the resulting composition is a very good approximation of the original one. These technical tools are then applied to prove a theorem about critical circle maps.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 1990
 arXiv:
 arXiv:math/9201274
 Bibcode:
 1992math......1274S
 Keywords:

 Mathematics  Dynamical Systems