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The Swiss Federal Office of Topography is leading a project for the determination of correct agricultural surfaces. As a part of this project, a Digital Terrain Model and a Digital Surface Model is being generated using airborne laser scanning methods. These two models must achieve a height accuracy of 50cm and a mean density of 1 point per m 2. One of the… (More)
The strange sets which arise in deterministic low dimensional dynamical systems are analyzed in terms of (unstable) cycles and their eigenvalues. The general formalism of cycle expansions is introduced and its convergence discussed .
Cycle expansions are applied to a series of low dimensional dynamically generated strange sets: the skew Ulam map, the period-doubling repeller, the H enon-type strange sets and the irrational winding set for circle maps. These illustrate various aspects of the cycle expansion technique; convergence of the curvature expansions, approximations of generic… (More)
We compute the decay of the autocorrelation function of the observable |v x | in the Sinai billiard and of the observable v x in the associated Lorentz gas with an approximation due to Baladi, Eckmann and Ruelle. We consider the standard configuration where the disks is centered inside a unit square. The asymptotic decay is found to be C(t) ∼ c(R)/t. An… (More)
We claim that looking at probability distributions of finite time largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincaré recurrences in the-quite-delicate case of dynamical systems with weak… (More)
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself through intermittency, dynamics where long periods of nearly regular motions are interrupted by irregular chaotic bursts.… (More)
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical appearance of phase transitions in the spectrum of transport exponents is explained. Periodic orbit theory of strongly… (More)
In this work we applied to bidimensional chaotic maps the numerical method proposed by Ginelli et al.  that allows to calculate in each point of an orbit the vectors tangent to the (stable/unstable) invariant manifolds of the system, i.e. the so called covariant Lyapunov vectors (CLV); through this knowledge it is possible to calculate the transversal… (More)
We present a series of results on deterministic transport in chaotic system, obtained in the framework of periodic orbits theory. The emphasis is on intermittent systems, where deviations from complete chaos may induce anomalies on the asymptotic moments' growth.