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Description: |
Flows of nonautonomous nonlinear ODEs are difficult to deal in
general, since
a nonautonomous vector field do not commute at different instants of time.
We will show
that vector fields and flows as differential geometry objects can be
regarded
as linear operators in a Fréchét space, allowing the construction of a well
suited linear calculus.
In particular, nonlinear control problems can be successfully manipulated
using these tools,
giving new results in Lyapunov stability or integrability of subriemannian
geodesics.
Many of their proprieties and relations can be nicely formulated using
special non-associative algebras as shuffle algebras, chronological
algebras and zinbiel
algebras. If we have time, we will also present a formal version of this
calculus on a Hopf algebra.
KEYWORDS: non-associative algebras, differential equations, free Lie
algebras, nonlinear control theory
Area(s):
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