Numerical computation of dichotomy rates and projectors in discrete time | Zendy

Thorsten Hüls | Zendy

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Numerical computation of dichotomy rates and projectors in discrete time

Author(s) -

Thorsten Hüls

Publication year - 2009

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2009.12.109

Subject(s) - mathematics , exponential dichotomy , computation , least squares function approximation , attractor , exponential function , interval (graph theory) , mathematical analysis , boundary value problem , boundary (topology) , orbit (dynamics) , differential equation , combinatorics , algorithm , statistics , estimator , aerospace engineering , engineering

We introduce a characterization of exponential dichotomies for linear difference equations that can be tested numerically and enables the approximation of dichotomy rates and projectors with high accuracy. The test is based on computing the bounded solutions of a specific inhomogeneous difference equation. For this task a boundary value and a least squares approach is applied. The results are illustrated using Henon's map. We compute approximations of dichotomy rates and projectors of the variational equation, along a homoclinic orbit and an orbit on the attractor as well as for an almost periodic example. For the boundary value and the least squares approach, we analyze in detail errors that occur, when restricting the infinite dimensional problem to a finite interval.

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