TY  - JOUR
A1  - Baptista, Murilo da Silva
A1  - Grebogi, Celso
A1  - Koberle, Roland
T1  - Dynamically multilayered visual system of the multifractal fly
JF  - Physical review letters
Y1  - 2006
U6  - https://doi.org/10.1103/PhysRevLett.97.178102
SN  - 0031-9007
VL  - 97
IS  - 17
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Feudel, Fred
A1  - Witt, Annette
A1  - Gellert, Marcus
A1  - Kurths, Jürgen
A1  - Grebogi, Celso
A1  - Sanjuan, Miguel Angel Fernandez
T1  - Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos
N2  - We study Hamiltonian chaos generated by the dynamics of passive tracers moving in a two-dimensional fluid flow and describe the complex structure formed in a chaotic layer that separates a vortex region from the shear flow. The stable and unstable manifolds of unstable periodic orbits are computed. It is shown that their intersections in the Poincare map as an invariant set of homoclinic points constitute the backbone of the chaotic layer. Special attention is paid to the finite time properties of the chaotic layer. In particular, finite time Lyapunov exponents are computed and a scaling law of the variance of their distribution is derived. Additionally, the box counting dimension as an effective dimension to characterize the fractal properties of the layer is estimated for different duration times of simulation. Its behavior in the asymptotic time limit is discussed. By computing the Lyapunov exponents and by applying methods of symbolic dynamics, the formation of the layer as a function of the external forcing strength, which in turn represents the perturbation of the originally integrable system, is characterized. In particular, it is shown that the capture of KAM tori by the layer has a remarkable influence on the averaged Lyapunov exponents. (C) 2004 Elsevier Ltd. All rights reserved
Y1  - 2005
ER  - 
TY  - JOUR
A1  - Viana, Ricardo L.
A1  - Barbosa, José R. R.
A1  - Grebogi, Celso
T1  - Unstable dimension variability and codimension-one bifurcations of two-dimensional maps
N2  - Unstable dimension variability is a mechanism whereby an invariant set of a dynamical system, like a chaotic attractor or a strange saddle, loses hyperbolicity in a severe way, with serious consequences on the shadowability properties of numerically generated trajectories. In dynamical systems possessing a variable parameter, this phenomenon can be triggered by the bifurcation of an unstable periodic orbit. This Letter aims at discussing the possible types of codimension-one bifurcations leading to unstable dimension variability in a two-dimensional map, presenting illustrative examples and displaying numerical evidences of this fact by computing finite-time Lyapunov exponents. (C) 2004 Elsevier B.V. All rights reserved
Y1  - 2004
SN  - 0375-9601
ER  - 
TY  - JOUR
A1  - Lai, Ying Cheng
A1  - Nagai, Y.
A1  - Grebogi, Celso
T1  - Characterization of the natural measure by unstable periodic orbits in chaotic attractors
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Hunt, Brain R.
A1  - Grebogi, Celso
A1  - Barreto, Ernest
A1  - Yorke, James A.
T1  - From high dimensional chaos to stable periodic orbits : the structure of parameter space
Y1  - 1997
ER  - 
TY  - JOUR
A1  - Kraut, Suso
A1  - Feudel, Ulrike
A1  - Grebogi, Celso
T1  - Preference of attractors in noisy multistable systems
Y1  - 1999
ER  -