| Abstract: |
| Computer-assisted proofs combine analytical arguments, rigorous numerics, and
validated error bounds to turn high-precision computations into fully
mathematical results. Improved analytic arguments lead directly to stronger and
more efficient computer-assisted proofs, by producing less restrictive
validation criteria and increasing the applicability of CAPs to concrete
dynamical systems. In this talk, we discuss this paradigm in the context of
KAM theory from the perspective of parameterization methods, where a posteriori
invariance equations provide a natural framework to validate numerically
computed invariant tori. We present new results in the form of more refined
estimates, leading to more effective validation procedures.
This is joint work with Jordi-Llu\`is Figueras (Uppsala University). |
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