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… 
View via Publisher
doi.org
24 Citations
Highly Influential Citations
3
Background Citations
11
Methods Citations
5
Results Citations
2

Figures from this paper

24 Citations

Trivial dynamics for a class of analytic homeomorphisms of the plane

A homeomorphism of the plane $h$ has trivial dynamics if every positive orbit $\{ h^n (p)\}_{n\geq 0}$ is either convergent (to a fixed point) or divergent (to infinity). The main result of this …

Unstable manifold, Conley index and xed points of ows I

We study dynamical and topological properties of the unstable manifold of isolated invariant compacta of flows. We show that some parts of the unstable manifold admit sections carrying a considerable…

Unstable manifold, Conley index and fixed points of flows

Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding

Existence of Coexistence States: A Generic Property for Cyclic 3-Dimensional Competitive Systems

Abstract In this paper we consider the class C ( T ) of all dissipative 3-dimensional T-periodic Kolmogorov competitive and cyclic systems such that the trivial solution is a source, and we prove…

Simple dynamics in non-monotone Kolmogorov systems

In this paper we analyse the global dynamical behaviour of some classical models in the plane. Informally speaking we prove that the folkloric criteria based on the relative positions of the…

Exclusion and dominance in discrete population models via the carrying simplex

This paper is devoted to show that Hirsch's results on the existence of a carrying simplex are a powerful tool to understand the dynamics of Kolmogorov models. For two and three species, we prove…

On the equivalent classification of three-dimensional competitive Atkinson/Allen models relative to the boundary fixed points

We study the fixed point index on the carrying simplex of the competitive map. The sum of the indices of the fixed points on the carrying simplex for the three-dimensional competitive map is unit.…

A Note for Cyclic 3-Dimensional Competitive Systems

In this paper we consider the class C of all T-periodic competitive and dissipative 3-dimensional systems which have a cyclic in the boundary and such that the origin is a source. We use the ideas in…

On the structure of the set of bounded solutions on a periodic Liénard equation

We describe the dynamics of a class of second order periodic differential equations whose main feature is a monotone nonlinearity. It is proved that the set of bounded solutions is homeomorphic to…

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…

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

An exclusion principle for periodic competitive systems in three dimensions

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