Tucker, Warwick A rigorous ODE solver and Smale’s 14th problem. (English) Zbl 1047.37012 Found. Comput. Math. 2, No. 1, 53-117 (2002). 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. Reviewer: Faouzi Lakrad (Stuttgart) Cited in 2 ReviewsCited in 155 Documents MSC: 37C10 Dynamics induced by flows and semiflows 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 65G30 Interval and finite arithmetic Keywords:ODE solver; interval arithmetic; Lorenz equation; normal form; strange attractor Software:PROFIL/BIAS; RODES PDFBibTeX XMLCite \textit{W. Tucker}, Found. Comput. Math. 2, No. 1, 53--117 (2002; Zbl 1047.37012)