**Title:** Kneading sequences for double standard maps

**Speaker:** Professor Ana Rodrigues

**Speaker Info:** IUPUI

**Brief Description:**

**Special Note**:

**Abstract:**

Recently, in joint work with M. Misiurewicz weinvestigated the family of double standard maps of the circle

onto itself, given by

f_{a,b}(x) = 2x + a + \frac{b}{\pi}\sin(2\pi x) (mod 1).

Similarly to the family of Arnold standard maps of the

circle,

A_{a,b}(x)=x+a+\frac{b}{2\pi}\sin(2\pi x) (mod 1),

if 0 < b \le 1 then any such map has at most one attracting periodic

orbit. The values of the parameters for which such an orbit exists are

grouped into Arnold tongues. These results lead to an

introductory study of the symbolic dynamics for the double standard

family in joint work with M. Benedicks.

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