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A rigorous ODE solver and Smale’s 14th problem. (English) Zbl 1047.37012

The author presents an algorithm for computing rigorous solutions for ordinary differential equations. The algorithm is broken down into two main parts: A local part, which is based on normal form theory, and a global part, which involves interval arithmetic with directed rounding and partitioning process. As an application of this algorithm, the author proves that the Lorenz equations support a robust strange attractor and that its flow admits a unique SRB measure, whose support coincides with the attractor.

MSC:

37C10 Dynamics induced by flows and semiflows
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
65G30 Interval and finite arithmetic

Software:

PROFIL/BIAS; RODES
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