A Rigorous ODE Solver and Smale’s 14th Problem

By W. Tucker. Foundations of Computational Mathematics, 2002

545 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/63ffec4a79be96ff9bd25562fee75da98e48e8d5

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Citations in the corpus

A new twist on Lorenz links (2007, methodology): “Later, Tucker [24] rigorously justified this geometric model for Lorenz’s original parameters.”
Climate Sensitivity via a Nonparametric Fluctuation–Dissipation Theorem (2011, background): “The forcing of trajectories toward the strange attractor of the Lorenz model is exceptionally strong in comparison with movement along the attractor itself (Tucker 2002).”
Riemann Surface Laminations with Singularities (2008, background): “For a proof that this is a strange attractor as indicated by computer pictures, see Warwick [63].”
Data Assimilation: A Mathematical Introduction (2015, background): “Furthermore, a subsequent computer assisted proof demonstrated rigorously that the ODE does indeed exhibit chaos [111, 112].”
Partial synchronization: from symmetry towards stability (2002, background): “This attractor contains the origin (e.g., see [ 51 ]).”
Singular-hyperbolic attractors are chaotic (2005, background): “Recently Tucker [46] proved that the flow defined by the Lorenz equations [26] exhibits a singular-hyperbolic attractor.”
The Lorenz Attractor is Mixing (2004, methodology): “A combination of results obtained over the last 25 years [1, 14, 20, 25, 30] and culminating in the work of Tucker [27, 28 ] gives the following statement (see [26, 29] for detailed surveys):”
Central limit theorems and invariance principles for Lorenz attractors (2007, background): “W. Tucker, ‘A rigorous ODE solver and Smale’s 14th problem’, Found.”
Validated Explicit and Implicit Runge-Kutta Methods (2016, background): “Nevertheless, in many applications, as for example [22, 7, 16, 41], an approximation of the solution is not sufficient and a bound of the exact solution is mandatory.”
Dynamics and Control at Feedback Vertex Sets. I: Informative and Determining Nodes in Regulatory Networks (2013, background): “Chaoticity has been proved for suitable parameters; see [26,37] and the earlier references there.”