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A procedure for finding numerical trajectories on chaotic saddles. (English) Zbl 0728.58027
The authors consider a diffeomorphism F of the plane and a compact region R containing no attractors of F. It is supposed that R contains a chaotic invariant set of F.
They construct a numerical method for finding trajectories of F which remain in R for arbitrarily long time. The method is based on PIM (Proper Interior Maximum) triples of points (a,b,c) in R, i.e. such that 1) c is an interior point of the line segment joining a and b; 2) the escape time of c from R is greater than both escape times of a and b.
It is shown that a procedure based on PIM triples converges in ideal situations. Results of applications of the method for the Smale horseshoe map, for the Lorenz equation, for a periodically perturbed pendulum are discussed.

MSC:
37D99 Dynamical systems with hyperbolic behavior
65L99 Numerical methods for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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