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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References

SHOWING 1-10 OF 11 REFERENCES

An extension of the results of hirsch on systems of differential equations which are competitive or cooperative

A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative). The…

Systems of differential equations which are competitive or cooperative: III. Competing species

For pt.II, see J. Math. Anal., vol.16, p.423 (1985). Persistent trajectories of the n-dimensional system xi=xiNi(x1, . . ., xn), xi>or=0, are studied under the assumptions that the system is…

Competition systems with periodic coefficients: A geometric approach

The classical two-species competition system is modified to include coefficients which are time-periodic with the same period. We show first that all (nonnegative) solutions converge to a periodic…

An exclusion principle for periodic competitive systems in three dimensions

Théoréme de translation plane de brouwer et généralisations du théoréme de Poincaré-Birkhoff

On the differential equations of species in competition

  • S. Smale
  • Biology
    Journal of mathematical biology
  • 1976
SummaryIt is shown that the ordinary differential equation commonly used to describe competing species are compatible with any dynamical behavior provided the number of species in very large.

The ore me de translation plane de Brouwer et ge ne ralisations du the ore me de Poincare Birkhoff, Topology

  • 1994

On the Number of Positive Periodic Solutions for Planar Competing Lotka-Volterra Systems

By:DS . Date:03:07:01 . Time:04:41 LOP8M. V8.0. Page 01:01 Codes: 2669 Signs: 960 . Length: 45 pic 0 pts, 190 mm REFERENCES

  • By:DS . Date:03:07:01 . Time:04:41 LOP8M. V8.0. Page 01:01 Codes: 2669 Signs: 960 . Length: 45 pic 0 pts, 190 mm REFERENCES

On the number of positive periodic solutions for planar competing Lokta

  • Volterra systems, J. Math. Anal. Appl
  • 1995