Computer-assisted proofs in nonlinear analysis
by
Jan Bouwe van den Berg
,
Maxime Breden
,
Olivier Hénot
,
Jean-Philippe Lessard
,
Jason D. Mireles James
Welcome
Software installation
Module 1: finite-dimensional problems
Finite-dimensional problems
Exercise 1:
Operator norms
Exercise 2:
Back to period 3 implies chaos
Exercise 3:
Rigorous computation of an eigenpair
Exercise 4:
Rigorous inverse of a matrix
Exercise 5:
Rigorous control of the entire spectrum
Exercise 6:
Toward rigorous continuation
Module 2: algebraic equations
Inverse
Square root
Module 3: Taylor integration
Taylor integration
Module 4: periodic orbits
Periodic orbits
Module 5: invariant manifolds of equilibria
Parameterization method
Lorenz system
Exercise 1:
Stable and unstable manifolds
Exercise 1:
2D manifold
Periodic orbits