NUMERICAL COMPUTATION OF DICHOTOMY RATES AND PROJECTORS IN DISCRETE TIME
Hüls, Thorsten
Hüls
Thorsten
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.
12
1
109-131
109-131
AMER INST MATHEMATICAL SCIENCES
2009