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The Newton iteration from the point of view of Thurston theory and root finding

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Speaker: 
Dierk Schleicher
Affiliation: 
Jacobs University Bremen
Date: 
Wed, 2018-07-04 09:00 - 09:50
Location: 
MPIM Lecture Hall

We describe the dynamical system generated by Newton’s root-finding method from the point of view of Thurston’s characterization theory of rational maps, leading to a complete classification of all postcritically finite Newton maps, and outline an extension to a classification of all Newton maps (postcritically finite or not). We also discuss Newton’s method from the point of view of root finding; it has successfully found all roots of polynomials of degrees greater than 10^9.

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