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Chaotic dynamics in the basin of attraction boundary via non-transversal intersections

Paper Authors:

Ernest Fontich,

Antonio Garijo,

Xavier Jarque

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Key Details

Proves existence of transversal homoclinic points for non-smooth map

Shows boundary of basin of attraction contains chaotic invariant set

Adapts Smale-Birkhoff theorem to non-smooth setting

Map lacks smooth invertibility and global diffeomorphism properties

AI generated summary

Chaotic dynamics in the basin of attraction boundary via non-transversal intersections

This paper analytically proves the existence of transversal homoclinic points and a chaotic invariant Cantor set on the boundary of the basin of attraction for a non-globally smooth diffeomorphism map related to the Secant method. The map lacks key properties like smooth invertibility, but the authors adapt tools like the Smale-Birkhoff theorem to show conjugacy with a full shift map on the chaotic set.

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