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nlin.CD2000

Semiclassical surface of section perturbation theory

Oleg Zaitsev

We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such sy…

nlin.CD2000★ 75 cited

Rectification of current in ac-driven nonlinear systems and symmetry properties of the Boltzmann equation

O. Yevtushenko, S. Flach, Y. Zolotaryuk +1

We study rectification of a current of particles moving in a spatially periodic potential under the influence of time-periodic forces with zero mean value. If certain time-space sy…

nlin.CD2000★ 22 cited

Linear and nonlinear information flow in spatially extended systems

Massimo Cencini, Alessandro Torcini

Infinitesimal and finite amplitude error propagation in spatially extended systems are numerically and theoretically investigated. The information transport in these systems can be…

nlin.CD2000★ 7 cited

Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics

M. Brack, M. Sieber, S. M. Reimann

We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the…

nlin.CD2000★ 16 cited

The Quantum-Classical Correspondence in Polygonal Billiards

Jan Wiersig

We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states…

nlin.CD2000★ 83 cited

Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity

G. Widman, T. Schreiber, B. Rehberg +2

We investigate several quantifiers of the electroencephalogram (EEG) signal with respect to their ability to indicate depth of anesthesia. For 17 patients anesthetized with Sevoflu…

nlin.CD2000★ 33 cited

Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

Hinke Osinga, Jan Wiersig, Paul Glendinning +1

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dyn…

nlin.CD2000★ 7 cited

Translationally invariant cumulants in energy cascade models of turbulence

Hans C. Eggers, Thomas Dziekan, Martin Greiner

In the context of random multiplicative energy cascade processes, we derive analytical expressions for translationally invariant one- and two-point cumulants in logarithmic field a…

nlin.CD2000★ 26 cited

Exit-Times and {\Large }-Entropy for Dynamical Systems, Stochastic Processes, and Turbulence

M. Abel, L. Biferale, M. Cencini +3

We present a comprehensive investigation of -entropy, , in dynamical systems, stochastic processes and turbulence. Particular emphasis is devoted on a recently proposed ap…

nlin.CD2000★ 132 cited

Chaos or Noise - Difficulties of a Distinction

M. Cencini, M. Falcioni, H. Kantz +2

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant m…

nlin.CD2000★ 20 cited

Singular continuous spectra in a pseudo-integrable billiard

Jan Wiersig

The pseudo-integrable barrier billiard invented by Hannay and McCraw [J. Phys. A 23, 887 (1990)] -- rectangular billiard with line-segment barrier placed on a symmetry axis -- is g…

nlin.CD2000★ 9 cited

Spectral statistics in chaotic systems with a point interaction

Martin Sieber

We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassica…

nlin.CD2000★ 14 cited

Relation between coupled map lattices and kinetic Ising models

F. Schmuser, W. Just, H. Kantz

A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal pertur…

nlin.CD2000★ 4.6k cited

Measuring Information Transfer

Thomas Schreiber

An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distin…

nlin.CD2000★ 13 cited

Local estimates for entropy densities in coupled map lattices

Eckehard Olbrich, Rainer Hegger, Holger Kantz

We present a method to derive an upper bound for the entropy density of coupled map lattices with local interactions from local observations. To do this, we use an embedding techni…

nlin.CD2000★ 69 cited

Modulated Amplitude Waves and the Transition from Phase to Defect Chaos

Lutz Brusch, Martin G. Zimmermann, Martin van Hecke +2

The mechanism for transitions from phase to defect chaos in the one-dimensional complex Ginzburg-Landau equation (CGLE) is presented. We introduce and describe periodic coherent st…