C. Letellier & G. Gouesbet
Topological characterization of a system with high-order symmetries : the proto-Lorenz system,
Physical Review E, 52 (5), 4754-4761, 1995.
Topological characterization of the Lorenz attractor taking into account the two-order equivariance of the vector field has been recently proposed by introducing a fundamental domain (typically a wing) and one copy of it. The present paper generalizes this approach to n-order equivariant systems. The general procedure is illustrated by taking a specific example, namely the so-called proto-Lorenz system which is derived from the Lorenz one. It is shown that symmetric attractors are tiled by n representations of a fundamental domain and that fundamental linking numbers therefore have to be introduced to conveniently validate the template.
C. Letellier, L. Le Sceller, P. Dutertre, G. Gouesbet, Z. Fei & J. L. Hudson
Topological Characterization and Global Vector Field Reconstruction from experimental electrochemical system,
Journal of Physical Chemistry, 99, 7016-7027, 1995. Online
A complete study of a copper electrodissolution experiment is achieved. The asymptotic motion settles down on a strange chaotic attractor which may be embedded in a 3D reconstructed space. In a 2D PoincarC section the attractor is found to be topologically equivalent to a 1D map, and its orbit spectrum is governed by the unimodal order. A set of equations which suitably model the experiment is extracted by a global vector field reconstruction method. The attractor obtained by integrating the reconstructed system is topologically equivalent to the original attractor. It is shown that the reconstructed model represents the dynamics without taking into account the effect of the dynamical noise on the experiment.
C. Letellier, L. Le Sceller, E. Maréchal, P. Dutertre, B. Maheu, G. Gouesbet, Z. Fei & J. L. Hudson
Global vector field reconstruction from a chaotic experimental signal in copper electrodissolution,
Physical Review E, 51 (5), 4262-4266, 1995. Onine
A successful global vector field reconstruction from experimental data that exhibit a chaotic behavior is obtained. Data arise from a copper electrodissolution. The reconstructed set of equations is checked by using a topological characterization.
C. Letellier, P. Dutertre & B. Maheu
Unstable periodic orbits and templates of the Rössler system: toward a systematic topological characterization,
Chaos, 5 (1), 272-281, 1995. Online
The Rössler system has been exhaustively studied for parameter values (a in [0.33,0.557],b=2,c=4). Periodic orbits have been systematically extracted from Poincare maps and the following problems have been addressed: i) all low order periodic orbits are extracted, ii) encoding of periodic orbits by symbolic dynamics (from 2 letters up to 11 letters) is achieved, iii) some rules of growth and of pruning of the periodic orbits population are obtained, and iv) the templates of the attractors are elaborated to characterize the attractors topology.