RT Journal Article
T1 Lp(μ) estimation of tangent maps
A1 Mera Rivas, María Eugenia
A1 Morán Cabré, Manuel
AB We analyze under what conditions the best Lp(μ)-linear fittings of the action of a mapping f on small balls give reliable estimates of the tangent map Df. We show that there is an inverse relationship between the conditions on the regularity, in terms of local densities, of the measure μ and the smoothness of the mapping f which are required to ensure the goodness of the estimates. The above results can be applied to the estimation of tangent maps in two empirical settings: from finite samples of a given probability distribution on IRⁿ and from finite orbits of smooth dynamical systems. As an application of the results of this paper we obtain sufficient conditions on the measure μ to ensure the convergence of Eckmann and Ruelle algorithm for computing the Liapunov exponents of smooth dynamical systems.
PB Elsevier
SN 0022-247X
YR 1999
FD 1999
LK https://hdl.handle.net/20.500.14352/60446
UL https://hdl.handle.net/20.500.14352/60446
LA eng
DS Docta Complutense
RD 28 abr 2024