Baker Kearfott, University of Southwestern Louisiana
Properties of dynamical systems are often specified by properties
of solutions to nonlinear systems of equations. For example, bifurcation
points correspond to parameter values in a parametrized nonlinear
system where the number of such solutions changes.
With interval computations, computer arithmetic can be used to
rigorously prove that such dynamical systems have certain properties.
The following contexts will be highlighted:
Incorporation of interval arithmetic in path-following algorithms
to verify continuation along a single mathematical path.
Use of interval arithmetic to compute the topological degree
of a mapping.
Use of interval arithmetic to verify a particular value of the
topological degree of a mapping.
Use of interval arithmetic to rigorously find all solutions to
a nonlinear system of equations within a particular region of
space (finite or infinite-dimensional).
The relative difficulty and practicality of each of these tasks
will be discussed.
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