@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{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{SchwarzSpahnGrebogietal.1999,
  author    = {Schwarz, Udo and Spahn, Frank and Grebogi, Celso and Kurths, J{\"u}rgen and Petzschmann, Olaf},
  title     = {Length scales of clustering in granular gases},
  year      = {1999},
  language  = {en}
}
@article{SauerGrebogiYorke1997,
  author    = {Sauer, T. and Grebogi, Celso and Yorke, J. A.},
  title     = {How long do numerical chaotic solutions remain valid?},
  year      = {1997},
  language  = {en}
}
@article{RosaHayesGrebogi1997,
  author    = {Rosa, Epaminondas and Hayes, S. and Grebogi, Celso},
  title     = {Noise filtering in communication with chaos},
  year      = {1997},
  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}
}
@article{LetellierAbrahamShepelyanskyetal.2021,
  author    = {Letellier, Christophe and Abraham, Ralph and Shepelyansky, Dima L. and Rossler, Otto E. and Holmes, Philip and Lozi, Rene and Glass, Leon and Pikovsky, Arkady and Olsen, Lars F. and Tsuda, Ichiro and Grebogi, Celso and Parlitz, Ulrich and Gilmore, Robert and Pecora, Louis M. and Carroll, Thomas L.},
  title     = {Some elements for a history of the dynamical systems theory},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {31},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {5},
  publisher = {AIP Publishing},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/5.0047851},
  pages     = {20},
  year      = {2021},
  abstract  = {Writing a history of a scientific theory is always difficult because it requires to focus on some key contributors and to "reconstruct" some supposed influences. In the 1970s, a new way of performing science under the name "chaos" emerged, combining the mathematics from the nonlinear dynamical systems theory and numerical simulations. To provide a direct testimony of how contributors can be influenced by other scientists or works, we here collected some writings about the early times of a few contributors to chaos theory. The purpose is to exhibit the diversity in the paths and to bring some elements-which were never published-illustrating the atmosphere of this period. Some peculiarities of chaos theory are also discussed.},
  language  = {en}
}
@article{LaiNagaiGrebogi1997,
  author    = {Lai, Ying Cheng and Nagai, Y. and Grebogi, Celso},
  title     = {Characterization of the natural measure by unstable periodic orbits in chaotic attractors},
  year      = {1997},
  language  = {en}
}
@article{LaiGrebogiKurths1999,
  author    = {Lai, Ying Cheng and Grebogi, Celso and Kurths, J{\"u}rgen},
  title     = {Modeling of deterministic chaotic systems},
  year      = {1999},
  language  = {en}
}