Reference

History of chaos theory

From the three-body problem to reservoir computing, roughly 130 years of mathematical and physical work that turned a curiosity into a working discipline.

1. 1890s

   Henri Poincaré, working on the three-body problem, finds that small differences in initial conditions can produce wildly different orbital fates. Implicit discovery of sensitivity dependence.

2. 1898

   Jacques Hadamard studies geodesics on negatively curved surfaces: first rigorous example of dynamical exponential divergence.

3. 1918-1930s

   George Birkhoff develops ergodic theory and proves the Poincaré recurrence theorem in modern form. Gaston Julia and Pierre Fatou study iteration of rational functions on the complex plane.

4. 1944

   Mary Cartwright and J. E. Littlewood analyse the forced van der Pol oscillator, finding what would later be recognised as chaos.

5. 1960s

   Steve Smale formalises the horseshoe map; Edward Lorenz at MIT discovers his three-equation atmospheric model and the butterfly effect. Vladimir Arnold studies hyperbolic toral automorphisms.

6. 1963

   Lorenz publishes 'Deterministic Nonperiodic Flow' in J. Atmos. Sci.: atomic event in the history of chaos theory.

7. 1971

   David Ruelle and Floris Takens propose strange attractors as the right mathematical object for turbulence.

8. 1975

   Tien-Yien Li and James Yorke publish 'Period three implies chaos' and coin the term 'chaos' in its modern mathematical sense.

9. 1976

   Robert May's Nature review 'Simple mathematical models with very complicated dynamics' makes the logistic map famous. Michel Hénon's two-dimensional mapping and Otto Rössler's single-scroll system appear within months.

10. 1978

    Mitchell Feigenbaum publishes universality and the constants α, δ for period-doubling cascades.

11. 1979

    Boris Chirikov publishes his standard map study, founding Hamiltonian chaos. Kensuke Ikeda's optical ring-cavity equation.

12. 1983

    Leon Chua designs the first chaos-on-purpose electronic circuit. Grassberger-Procaccia algorithm for correlation dimension published.

13. 1981-1985

    Floris Takens proves the delay-embedding theorem; Adrien Douady and John Hubbard show that the Mandelbrot set is connected; Wolf et al. publish the Lyapunov-from-time-series algorithm.

14. 1987

    James Gleick publishes 'Chaos: Making a New Science'; chaos enters popular culture.

15. 1990

    Ott-Grebogi-Yorke chaos control; Pecora-Carroll synchronisation. The chaos engineering era begins.

16. 1991

    Mitsuhiro Shishikura proves the Mandelbrot-set boundary has Hausdorff dimension 2.

17. 1992

    K. Pyragas's continuous time-delay feedback control; B. Banks et al. clarify Devaney's chaos definition.

18. 1994

    Julien Sprott enumerates 19 simple chaotic flows. Henry Abarbanel et al. publish the practical embedding pipeline.

19. 2000s

    Reservoir computing matures (Jaeger 2001, Maass 2002); chaos-based cryptography becomes a sustained research area; multifractal analysis takes off; Gottwald-Melbourne 0-1 test (2004); Bandt-Pompe permutation entropy (2002).

20. 2010s-now

    Chaotic dynamics combined with neural-network methods for forecasting (Pathak et al. 2018), chaos in memristive circuits, and increasingly precise rigorous-numerics proofs of strange attractor existence.