Searching chaotic saddles in high dimensions

• DOI: 10.1063/1.4973235
• Publication Date: 2016-12-30T14:08:36Z
• Authors: M. Sala; J. C. Leitão; E. G. Altmann
• Keywords: Exponent

We propose new methods to numerically approximate non-attracting sets governing transiently-chaotic systems. Trajectories starting in a vicinity $\Omega$ of these escape finite time $\tau$ and the problem is find initial conditions ${\bf x} \in \Omega$ with increasingly large $\tau= \tau({\bf x})$. search points x}'$ $\tau({\bf x}')>\tau({\bf x})$ {\it domain} $\Omega$. Our first method considers domain size that decreases exponentially $\tau$, an exponent proportional largest Lyapunov $\lambda_1$. second anisotropic domains tangent} unstable manifold, where each direction scale as inverse corresponding expanding} singular value Jacobian matrix iterated map. show both outperform state-of-the-art Stagger-and-Step} (Sweet, Nusse, York, Phys. Rev. Lett. {\bf 86}, 2261, 2001) but only achieves efficiency independent for case high-dimensional systems multiple positive exponents. perform simulations chain coupled H\'enon maps up 24 dimensions ($12$ exponents). This suggests possibility characterizing also spatio-temporal