Celso Grebogi

Celso Grebogi FRSE (born 1947) is a Brazilian theoretical physicist who works in the area of chaos theory. He is one among the pioneers in the nonlinear and complex systems and chaos theory. Currently he works at the University of Aberdeen as the "Sixth Century Chair in Nonlinear and Complex Systems". He has done extensive research in the field of plasma physics before his work on the theory of dynamical systems. He and his colleagues (Edward Ott and James A. Yorke) have shown with a numerical example that one can convert a chaotic attractor to any one of numerous possible attracting time-periodic motions by making only small time-dependent perturbations of an available system parameter. This article is considered as one among the classic works in the control theory of chaos and their control method is known as the OGY method. He was listed in the 2016 Thomson Reuters Citation Laureates.^[1]

Research areas

Grebogi has worked in the fields of dynamics of nonlinear and complex systems including chaotic dynamics, fractal geometry, systems biology, fluid advection and relativistic quantum chaotic dynamics.

Edited books

Together with Miguel A. F. Sanjuán (Rey Juan Carlos University, Spain) he was the editor of the book Recent Progress In Controlling Chaos.

Honours and awards

In 2012 Grebogi was elected a Fellow of the Royal Society of Edinburgh.^[2]

References

• Grebogi, Celso; Ott, Edward; Yorke, James A. (1987-10-30). "Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics". Science. 238 (4827): 632–638. doi:10.1126/science.238.4827.632. ISSN 0036-8075.
• Ott, Edward; Grebogi, Celso; Yorke, James A. (1990-03-12). "Controlling chaos". Physical Review Letters. 64 (11): 1196–1199. doi:10.1103/PhysRevLett.64.1196. ISSN 0031-9007.
• Shinbrot, Troy; Grebogi, Celso; Yorke, James A.; Ott, Edward (1993). "Using small perturbations to control chaos". Nature. 363 (6428): 411–417. doi:10.1038/363411a0. ISSN 0028-0836.
• M. A. F. Sanjuán Recent progress in controlling chaos, World Scientific 2010

External links

• University of Maryland Webpage
• University of Aberdeen Webpage
• Google Scholar Page

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Chaos theory

Concepts

Core	Attractor Bifurcation Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space
Anosov diffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting dimension Correlation dimension Conservative system Ergodicity False nearest neighbors Hausdorff dimension Invariant measure Lyapunov stability Measure-preserving dynamical system Mixing Poincaré section Recurrence plot SRB measure Stable manifold Topological conjugacy
Theorems	Ergodic theorem Liouville's theorem Krylov–Bogolyubov theorem Poincaré–Bendixson theorem Poincaré recurrence theorem Stable manifold theorem Takens's theorem

Theoretical
branches

• Bifurcation theory
• Control of chaos
• Dynamical system
• Ergodic theory
• Quantum chaos
• Stability theory
• Synchronization of chaos

Chaotic
maps (list)

Discrete	Arnold's cat map Baker's map Complex quadratic map Coupled map lattice Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Irrational rotation Kaplan–Yorke map Langton's ant Logistic map Standard map Tent map Tinkerbell map Zaslavskii map
Continuous	Double scroll attractor Duffing equation Lorenz system Lotka–Volterra equations Mackey–Glass equations Rabinovich–Fabrikant equations Rössler attractor Three-body problem Van der Pol oscillator

Physical
systems

• Chua's circuit
• Convection
• Double pendulum
• Elastic pendulum
• FPUT problem
• Hénon–Heiles system
• Kicked rotator
• Multiscroll attractor
• Population dynamics
• Swinging Atwood's machine
• Tilt-A-Whirl
• Weather

Chaos
theorists

• Michael Berry
• Rufus Bowen
• Mary Cartwright
• Chen Guanrong
• Leon O. Chua
• Mitchell Feigenbaum
• Peter Grassberger
• Celso Grebogi
• Martin Gutzwiller
• Brosl Hasslacher
• Michel Hénon
• Svetlana Jitomirskaya
• Bryna Kra
• Edward Norton Lorenz
• Aleksandr Lyapunov
• Benoît Mandelbrot
• Hee Oh
• Edward Ott
• Henri Poincaré
• Itamar Procaccia
• Mary Rees
• Otto Rössler
• David Ruelle
• Caroline Series
• Yakov Sinai
• Oleksandr Mykolayovych Sharkovsky
• Nina Snaith
• Floris Takens
• Audrey Terras
• Mary Tsingou
• Marcelo Viana
• Amie Wilkinson
• James A. Yorke
• Lai-Sang Young

Related
articles

• Butterfly effect
• Complexity
• Edge of chaos
• Predictability
• Santa Fe Institute