nucleation

LIT-1997: Controlling chaos

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StatusUnavailable — searched 2026-11-03 for a lawful full text and none was reached, so it is not read and no NOTE is filed. OpenAlex and Unpaywall (noreply address) report it closed; PubMed has the abstract only. journals.aps.org returned a Cloudflare bot check (403) to this client, and was not tried again. The paper is one of PRL's fifty-year milestone letters; whether APS makes milestone letters free to read could not be confirmed, since the milestones page returned 403 and the Wayback Machine is blocked by this session's egress policy. If it is free, the owner can open journals.aps.org/prl/abstract/10.1103/PhysRevLett.64.1196, and this should be Unfetched. Yorke's own list of cited papers (yorke.umd.edu/cited100+.html) did not answer. Web searches found no author or course copy. CLAIM-541 and CLAIM-542 describe the method second-hand.
Version2
Tagscontrol-theory, complex-systems
Cited as “grounds” byCLAIM-533 — The sensitivity that formal chaos gives a will's dynamics is not control over them: in Kane's self-forming actions, chaotic amplification keeps the outcome open, but it magnifies the agent's efforts, uncontrolled fluctuations and outside inputs alike, so what would make the outcome the agent's is how its own control couples to the amplifying directions, relative to noise and to other parties' inputs and with what feedback, which sensitivity does not supply; and under weak noise what amplification touches lasts only where it reaches the slow modes, CLAIM-541 — Wu-wei is better read as control placed and timed where a system's own dynamics do most of the work than as the absence of control: Ott–Grebogi–Yorke control of chaos is a formal instance, in which small perturbations timed by the system's own wandering hold it on an unstable orbit, and the control, though small, continues for as long as the orbit is held; so reported effortlessness has at least three distinct sources, no conflict to override, conflict settled cheaply by learned accommodation, and conflict met as it arises by small well-timed feedback, which may feel alike and differ in mechanism, CLAIM-542 — Sensitivity does not fix the allocation or the authorship of control: linearized, every input reaches the final state through the same transition operator, ∂x_T/∂w_t = Φ(T, t)B_w(t), so systems with the same Lyapunov spectrum can differ arbitrarily in what an agent's own channel, an outside party's channel and noise each reach and at what least energy; and along one unstable direction a larger exponent λ lowers the least effort to reach a displacement, since W_T = b²(e^{2λT} − 1)/2λ grows with λ, while a constant open-loop input against white noise entering the same direction has terminal signal-to-noise ratio tending to (bu/σ)√(2/λ), which falls as λ grows, so only feedback that observes the state turns cheaper control into reliable direction

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Ott, E., Grebogi, C., Yorke, J. A. (1990). Controlling chaos. Physical Review Letters, 64(11), 1196-1199. doi:10.1103/PhysRevLett.64.1196.

Key takeaways

Not read. Nothing here reports the work’s findings; what the exchange’s replies said of it is unverified.

Standing in the record

The method the owner called “very wu-wei” (U17): small parameter perturbations, timed by the system’s own wandering, hold it on an unstable periodic orbit. The control is small but continues while the orbit is held. Grounds CLAIM-541 and CLAIM-542.

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