Periodic orbit theory of two coupled Tchebyscheff maps

@article{Dettmann2003PeriodicOT,
  title={Periodic orbit theory of two coupled Tchebyscheff maps},
  author={Carl P. Dettmann and UK D.LippolisUniversityofBristol and University of Bologna Italy},
  journal={Chaos Solitons \& Fractals},
  year={2003},
  volume={23},
  pages={43-54}
}

Figures and Tables from this paper

Scaling behavior of nonhyperbolic coupled map lattices.

  • S. GrooteC. Beck
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
A general 1st order perturbation theory is developed to analytically calculate the invariant one-point density, show that the density exhibits log-periodic oscillations in phase space, and obtain excellent agreement with numerical results.

Discrete symmetries of chaotic strings

Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. In this article we look at two important

Scaling properties of invariant densities of coupled Chebyshev maps

We study one-dimensional coupled map lattices consisting of diffusively coupled Chebyshev maps of N-th order. For small coupling constants a we determine the invariant 1-point and 2-point densities

Renormalization aspects of chaotic strings

Chaotic strings are a class of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. In this paper we

A coupling of three quadratic maps

Statistical mechanics of the vacuum

The vacuum is full of virtual particles which exist for short moments of time. In this paper we construct a chaotic model of vacuum fluctuations associated with a fundamental entropic field that

A first approach to the Galois group of chaotic chains

The definition, construction and generalisation of the Galois group of Chebyshev polynomials of high degree to the Galese group of chaotic chains is explained.

Information Shift Dynamics Described by Tsallis q = 3 Entropy on a Compact Phase Space

Recent mathematical investigations have shown that under very general conditions, exponential mixing implies the Bernoulli property. As a concrete example of statistical mechanics that are

References

SHOWING 1-10 OF 45 REFERENCES

Topological properties of linearly coupled expanding map lattices

We study topological aspects of the dynamics of one-dimensional lattices of coupled expanding maps of an interval, the coupling being a convolution by a sequence in l1(). Some conditions on the local

Discrete symmetries in periodic-orbit theory.

  • Robbins
  • Physics, Mathematics
    Physical review. A, General physics
  • 1989
The application of periodic-orbit theory to systems which possess a discrete symmetry is considered. A semiclassical expression for the symmetry-projected Green's function is obtained; it involves a

Floquet Spectrum of Weakly Coupled Map Lattices

Abstract: We consider weakly coupled analytic expanding circle maps on the lattice ℤD (for D≥ 1), with small coupling strength ε and summable decay of the two-sites coupling. We study the spectrum of

Dynamical Systems Approach to Turbulence

Introduction 1. Turbulence and dynamical systems 2. Phenomenology of turbulence 3. Reduced models for hydrodynamic turbulence 4. Turbulence and coupled map lattices 5. Turbulence in the complex

Theory and applications of coupled map lattices

Coupled map lattices renormalization group, universality and scaling in dynamics of coupled map lattices mean field approximations and Perron-Frobenius equations for coupled map lattices complex

Spontaneous synchronous discharges in hippocampal slices. Simulation and experiment

The conversion of chaotic oscillations into synchronous ones, which are typical for epileptiform discharges, is studied and the results obtained are in good agreement with those derived from hippocampal slices treated with picrotoxin.

Spatio Temporal Chaos and Vacuum Fluctuations of Quantized Fields

Chaotic Quantization of Field Theories Chaotic Strings Vacuum Energy of Chaotic Strings Phase Transitions and Spontaneous Symmetry Breaking Generalized Statistical Mechanics Approach Interaction