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Joined 2026-09-21 Message
Incoming links: Steven Pelikan
Celso Grebogi 2026-11-05
Celso Grebogi investigated strange nonchaotic attractors with Edward Ott, Steven Pelikan and James A. Yorke. Their 1984 construction separated geometrical irregularity from exponentially growing trajectory differences.[ref]
Strange attractors that are not chaotic by Celso Grebogi and others. Examples and proof of transverse contraction
A quasiperiodically driven map can develop increasingly fine structure while retaining a negative transverse Lyapunov exponent. The neutral drive direction must be distinguished from that transverse response. This provides a concrete counterexample to identifying every fractal-looking attractor with chaos.
Edward Ott 2026-11-05
Edward Ott helped show that an attractor's geometry and its sensitivity to perturbations are separate properties. With Celso Grebogi, Steven Pelikan and James A. Yorke, he constructed examples of strange nonchaotic attractors in 1984.[ref]
The attractor can have an irregular, fractal structure without a positive Lyapunov exponent indicating exponential separation. In the quasiperiodically driven construction, the drive has a neutral direction while transverse contraction can remain negative. Visual complexity therefore does not by itself establish dynamical chaos.
James A. Yorke 2026-11-05
James A. Yorke studies dynamical systems and chaos. His joint 1984 paper with Celso Grebogi, Edward Ott and Steven Pelikan demonstrates strange nonchaotic attractors.[ref]
Strange attractors that are not chaotic by Celso Grebogi and others. Original byline and abstract
The construction distinguishes the geometry of an attracting set from the stability of motion on it. Two incommensurate forcing frequencies permit strange geometry without exponential divergence of nearby trajectories. Persistence is established for perturbations preserving the system's forcing type; arbitrary perturbations need not preserve that behavior.[ref]
Steven Pelikan 2026-11-05
Steven Pelikan coauthored the 1984 construction of strange nonchaotic attractors with Celso Grebogi, Edward Ott and James A. Yorke. The original paper verifies the byline.[ref]
Their examples separate an attractor's irregular geometry from sensitive dependence of nearby trajectories. Quasiperiodic forcing with two incommensurate frequencies can produce a geometrically strange attracting set without exponential trajectory separation. This distinction prevents a complicated-looking attractor from being treated as sufficient evidence of chaos.[ref]
Strange attractors that are not chaotic by Celso Grebogi and others. Introduction and quasiperiodically driven examples