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Zbl 0997.37500
Davie, A.M.
The critical function for the semistandard map. (English)
[J] Nonlinearity 7, No.1, 219-229 (1994). ISSN 0951-7715; ISSN 1361-6544/e

Summary: For the semistandard map $F(x,y)=(x+y+ie^{ix}, y+ie^{ix})$, we consider the critical function $K_{\text{ss}}(\omega)$, defined as the radius of convergence of a series expansion of a complex invariant curve of rotation number $\omega$, and show that $\log K_{\text{ss}}(\omega)+2\sum q^{-1}_k\log q_{k+1}$ is bounded on the set of $\omega$ where it is well defined, where $\{q_k\}$ are the denominators of the convergents to the real number $\omega$. We discuss the implications for critical functions for the standard map.

MSC 2000:: *37C55 Periodic and quasiperiodic flows and diffeomorphisms

Cited in: Zbl 1175.37050

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