20 citations · 26 across the 9 of their papers we have counts for
9 papers
A computer-assisted proof of robust transitivity
Marisa Cantarino, Andy Hammerlindl, Warwick Tucker
We present computer-assisted proofs of partial hyperbolicity, existence of a blender and robust transitivity for diffeomorphisms on closed manifolds. These proofs are implemented f…
An algorithm to detect and rigorously verify blenders
Andy Hammerlindl, Natalia McAlister, Warwick Tucker
We present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorith…
Darboux-type center conditions for families of planar polynomial vector fields
Yovani Villanueva, Warwick Tucker
We study the center-focus problem for planar polynomial vector fields, which can be viewed as a local version of Hilbert's 16th problem. Based on a Lyapunov function approach, we e…
Nowhere coexpanding functions
Andrew Cook, Andy Hammerlindl, Warwick Tucker
We define a family of functions which we call "nowhere coexpanding functions" that is closed under composition and includes all functions with non-positive Schwarzian d…
The number of relative equilibria in the PCR4PB
Jordi-Lluís Figueras, Warwick Tucker, Piotr Zgliczynski
The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial…
Lower bounds on the Hausdorff dimension of some Julia sets
Artem Dudko, Igors Gorbovickis, Warwick Tucker
We present an algorithm for a rigorous computation of lower bounds on the Hausdorff dimensions of Julia sets for a wide class of holomorphic maps. We apply this algorithm to obtain…
A note on the convergence of parametrised non-resonant invariant manifolds
Tomas Johnson, Warwick Tucker
Truncated Taylor series representations of invariant manifolds are abundant in numerical computations. We present an aposteriori method to compute the convergence radii and error e…
Automated computation of robust normal forms of planar analytic vector fields
Tomas Johnson, Warwick Tucker
We construct an auto-validated algorithm that calculates a close to identity change of variables which brings a general saddle point into a normal form. The transformation is robus…
On a computer-aided approach to the computation of Abelian integrals
Tomas Johnson, Warwick Tucker
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are per…