A Verified ODE Solver and Smale's 14th Problem

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• Fabian Immler (Technische Universität München)
• Thursday 06 July 2017, 13:40-14:20
• Seminar Room 2, Newton Institute.

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Smale's 14th Problem is a conjecture about chaos in a
particular dynamical system, the Lorenz attractor. The problem was solved by
Warwick Tucker with a combination of regular analysis and a computer-assisted
part. The computer-assisted part yields numerical bounds on solutions of the
Lorenz ODE , which are required to certify chaos.

In this talk, I will present the current library of ODEs
and verified numerical methods in Isabelle/HOL, and how I use it for a formal
verification of the computer-assisted part of Tucker's proof.

This talk is part of the Isaac Newton Institute Seminar Series series.

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