Computational hyperbolicity (Q632360)

Nowadays, computers are quite often used for proving theorems whose direct analytic verification is not possible. The paper under review deals with the problem of computer assisted proof of hyperbolicity of a given set using a concept of semihyperbolicity. Taking into account that semihyperbolicity does not require the splitting of the space to be invariant, it can be directly and relatively easily verified through a direct numerical computation. For example, the authors prove hyperbolicity of the celebrated Hénon attractor associated with the Hénon map of the real plane into itself, \[ H_{a,b}:(x,y) \mapsto(a-x^{2}+by,x) , \] for \(a=5.4\) and \(b=-1\) in less than 10 seconds on a 2 GHz personal computer.