Konstantin L Kouptsov 2004 J. Phys. A: Math. Gen. 37 6491 doi:10.1088/0305-4470/37/25/005
Interval propagation method for finding trajectories of chaotic maps
Konstantin L Kouptsov
Show affiliationsThe algorithm for calculation of trajectories of chaotic maps, based on the interval analysis, is proposed. Each of the image points is constrained by enclosing it in a corresponding interval. Improvement of one of the constraints results in the chain of adjustments of other interval bounds propagating along the trajectory, eventually causing the constraints to converge. No knowledge of well-defined symbolic dynamics is necessary since the pruning rules and non-uniqueness of the symbolic path are automatically resolved. For cycles and fixed-end orbits the algorithm provides linear uniform convergence. The algorithm is demonstrated for the Hamiltonian system where existence of both positive and negative Lyapunov exponents allows introduction of a simple interval-contracting procedure.
- PACS
- MSC
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37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
- Subjects
- Dates
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Issue 25 (25 June 2004)
Received 18 November 2003, in final form 13 April 2004
Published 9 June 2004
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Interval propagation method for finding trajectories of chaotic maps
Konstantin L Kouptsov 2004 J. Phys. A: Math. Gen. 37 6491
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