By Saber N. Elaydi, Henrique Oliveira, Jose Manuel Ferreira, Joao F Alves

This quantity holds a set of articles in accordance with the talks provided at ICDEA 2007 in Lisbon, Portugal.

the quantity encompasses present themes on balance and bifurcation, chaos, mathematical biology, new release conception, nonautonomous platforms, and stochastic dynamical systems.

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Discrete Dynamics and Difference Equations: Proceedings of the Twelfth International Conference on Difference Equations and Applications

This quantity holds a set of articles in keeping with the talks offered at ICDEA 2007 in Lisbon, Portugal. the quantity encompasses present issues on balance and bifurcation, chaos, mathematical biology, new release conception, nonautonomous structures, and stochastic dynamical platforms.

Additional resources for Discrete Dynamics and Difference Equations: Proceedings of the Twelfth International Conference on Difference Equations and Applications

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3 and 4. We will say that a point x is attracted to A (where A can be a point or a compact set) if the trajectory of x converges to A, that is, the distance from the k-th image of x to A converges to 0 as k → ∞. When we say that a fixed point is orientation preserving or reversing, we mean the behavior of the map in a neighborhood of that point. 1. Let n ∈ H be the essential Nash map described above. (a) For all α, (0, 0) and (1, 1) are orientation preserving, topologically attracting fixed points and (1/2, 1/2) is a fixed point.

The similar statement for the SW quadrant follows from the symmetry of the map with respect to the diagonal. September 7, 2010 16:7 WSPC - Proceedings Trim Size: 9in x 6in 02 29 4. Making use of the symmetry By the results of the preceding section, the only trajectories with unknown behavior are those that go through both N W and SE quadrants. In order to investigate them, we consider rd ◦n in the N W and SE quadrants. This map commutes with rd because n does. Therefore, again looking at the N W and SE quadrants will be equivalent.

Assume that α > 2(1 + 2). Then for f the stable manifold W1s of q1 goes from (0, 0) (excluding this point) via q1 to a point on the right side of the square [0, 1]2 . The stable manifold W2s of q2 goes from (0, 0) (excluding this point) via q2 to a point on the upper side of the square [0, 1]2 . The trajectories of all points of the region between those manifolds converge to the fixed point q. The trajectories of all points below W 1s and all points to the left of W2s leave the square [0, 1]2 .

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