HOMEOMORPHISMS OF THE DISK WITH TRIVIAL DYNAMICS AND EXTINCTION OF COMPETITIVE SYSTEMS

@article{Campos1997HOMEOMORPHISMSOT,
  title={HOMEOMORPHISMS OF THE DISK WITH TRIVIAL DYNAMICS AND EXTINCTION OF COMPETITIVE SYSTEMS},
  author={Juan Campos and Rafael Ortega and Antonio Tineo},
  journal={Journal of Differential Equations},
  year={1997},
  volume={138},
  pages={157-170}
}
Let h be a homeomorphism of a closed two-dimensional disk D and let Fix(h) denote the set of fixed points of h. We say that h has trivial dynamics if the omega limit set of every orbit [h( p)]n # Z , p # D, is included in Fix(h). In general, the dynamics of a homeomorphism of the disk can be very intricate and one cannot expect this simple behavior unless additional assumptions are imposed. In this paper we shall assume that h is orientation-preserving and that all fixed points are on the… 

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