Talk:Blue sky catastrophe

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Origins of the idea

In "Foundations of Mechanics", Ralph Abraham and Jerrold E. Marsden, 2nd edition, Benjamin/Cummings 1978, there is a phase portrait labeled "blue-sky catastrophe" on page 566-567, and that picture credits Ruelle and Takens for coming up with the idea in 1971. The reference given (I have not checked it) is

"On the nature of turbulence", Comm. Math. Phys. 20 pp 167-192 and 23 pp 343-344.

While the idea is clearly not as fully developed as in the scholarpedia article, it does state the basic idea: "As μ approaches zero from the left, the period of the attracting closed orbit tends to infinity." The (rather simple) picture implies that the measure evaporates to zero.

It also gives two "modern refs" as

J.C. Alexander and J.A. Yorke 1978 "Global Hopf Bifurcation", Am. J. Math, "to appear" (I guess, not yet in print when the book came out)

RL Devaney 1978 "Blue sky catastrophes in reversible and Hamiltonian systems" (preprint) but google knows all: Indiana University Mathematics Journal 26 (1977), 247-263.

Please note that, by 1977, Devaney already has a published paper with this phrase in the title; you can google that one, it's on his website. linas (talk) 14:59, 11 March 2008 (UTC)[reply]