@article{BaptistaGrebogiKoberle2006,
  author    = {Baptista, Murilo da Silva and Grebogi, Celso and Koberle, Roland},
  title     = {Dynamically multilayered visual system of the multifractal fly},
  series = {Physical review letters},
  volume    = {97},
  journal   = {Physical review letters},
  number    = {17},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.97.178102},
  pages     = {4},
  year      = {2006},
  language  = {en}
}
@article{BaptistaKrautGrebogi2005,
  author    = {Baptista, Murilo da Silva and Kraut, Suso and Grebogi, Celso},
  title     = {Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors},
  issn      = {0031-9007},
  year      = {2005},
  abstract  = {We study Poincare recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is no longer supported solely by unstable periodic orbits of finite length inside it, but also by other special recurrent trajectories, located outside that region. The presence of the latter leads to a deviation of the distribution of the Poincare first return times from a Poissonian. Consequently, by taking into account the contribution of these special recurrent trajectories, a corrected estimate of the measure is obtained. This has wide experimental implications, as in the laboratory all returns can exclusively be observed for regions of finite size, and only unstable periodic orbits of finite length can be detected},
  language  = {en}
}
@article{FeudelWittGellertetal.2005,
  author    = {Feudel, Fred and Witt, Annette and Gellert, Marcus and Kurths, J{\"u}rgen and Grebogi, Celso and Sanjuan, Miguel Angel Fernandez},
  title     = {Intersections of stable and unstable manifolds : the skeleton of Lagrangian chaos},
  year      = {2005},
  abstract  = {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},
  language  = {en}
}
@article{VianaGrebogiPintoetal.2005,
  author    = {Viana, R. L. and Grebogi, Celso and Pinto, S. E. D. and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen},
  title     = {Bubbling bifurcation : loss of synchronization and shadowing breakdown in complex systems},
  year      = {2005},
  abstract  = {Complex dynamical systems with many degrees of freedom may exhibit a wealth of collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of coupled logistic maps to investigate the relationship between the loss of chaos synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization manifold. This has been confirmed by numerical diagnostics of synchronization and non-hyperbolic behavior, the latter using the statistical properties of finite-time Lyapunov exponents. (c) 2005 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{DeFreitasVianaGrebogi2004,
  author    = {De Freitas, M. S. T. and Viana, R. L. and Grebogi, Celso},
  title     = {Basins of attraction of periodic oscillations in suspension bridges},
  issn      = {0924-090X},
  year      = {2004},
  abstract  = {We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations},
  language  = {en}
}
@article{KarolyiTeldeMouraetal.2004,
  author    = {Karolyi, G. and Tel, Tomas and de Moura, A. P. S. and Grebogi, Celso},
  title     = {Reactive particles in random flows},
  issn      = {0031-9007},
  year      = {2004},
  abstract  = {We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically},
  language  = {en}
}
@article{VianaBarbosaGrebogi2004,
  author    = {Viana, Ricardo L. and Barbosa, Jos{\´e} R. R. and Grebogi, Celso},
  title     = {Unstable dimension variability and codimension-one bifurcations of two-dimensional maps},
  issn      = {0375-9601},
  year      = {2004},
  abstract  = {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},
  language  = {en}
}
@article{VianaGrebogiPintoetal.2003,
  author    = {Viana, R. L. and Grebogi, Celso and Pinto, Seds and Lopes, S. R. and Batista, A. M. and Kurths, J{\"u}rgen},
  title     = {Validity of numerical trajectories in the synchronization transition of complex systems},
  issn      = {1063-651X},
  year      = {2003},
  abstract  = {We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties},
  language  = {en}
}
@article{KarolyiPentekToroczkaietal.1998,
  author    = {Karolyi, Gy{\"o}rgy and Pentek, Aron and Toroczkai, Zolt{\´a}n and T{\´e}l, T{\´o}mas and Grebogi, Celso},
  title     = {Advection of active particles in open chaotic flows},
  issn      = {0031-9007},
  year      = {1998},
  language  = {en}
}
@article{PoonGrebogiFeudeletal.1998,
  author    = {Poon, L. and Grebogi, Celso and Feudel, Ulrike and Yorke, J. A.},
  title     = {Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors},
  year      = {1998},
  language  = {en}
}