Comparison of indicators of chaos based on the deviation vectors

Rio de Janeiro, Brasil

Congreso; XV Colóquio Brasileiro de Dinâmica Orbital; 2010

INPE, Brazil

<!-- #toc, .toc, .mw-warning { border: 1px solid #aaa; background-color: #f9f9f9; padding: 5px; font-size: 95%; } #toc h2, .toc h2 { display: inline; border: none; padding: 0; font-size: 100%; font-weight: bold; } #toc #toctitle, .toc #toctitle, #toc .toctitle, .toc .toctitle { text-align: center; } #toc ul, .toc ul { list-style-type: none; list-style-image: none; margin-left: 0; padding-left: 0; text-align: left; } #toc ul ul, .toc ul ul { margin: 0 0 0 2em; } #toc .toctoggle, .toc .toctoggle { font-size: 94%; }@media print, projection, embossed { body { padding-top:1in; padding-bottom:1in; padding-left:1in; padding-right:1in; } } body { font-weight:normal; font-family:´Times New Roman´; font-style:normal; text-decoration:none; text-indent:0in; text-align:left; widows:2; font-variant:normal; color:#000000; font-size:12pt; } table { } td { border-collapse:collapse; text-align:left; vertical-align:top; } p, h1, h2, h3, li { color:#000000; font-family:´Times New Roman´; font-size:12pt; margin-left:0.0000in; margin-right:0.0000in; text-align:left; vertical-align:normal; } *.body_text { font-weight:bold; text-align:center; } --> The aim of the present work is to study the reliability of several chaos indicators that are based on the evolution of the deviation vectors. In order to perfom this study we make several experiments on mappings, including the Lyapunov Indicator (LI), the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller Alignment Index (SALI), the Fast Lyapunov Indicator (FLI), the Dynamical Spectra of stretching numbers (SSN) and the corresponding Spectral Distance (SD) and the Relative Lyapunov Indicator (RLI), on a variant of Froeschlé´s 4D symplectic mapping and  two coupled standard mappings.  We also run some preliminary tests on flows. Using the simple model of Hénon-Heiles, the Orthogonal Fast Lyapunov Indicator (OFLI) and the Generalized Alignment Index (GALI) were included in the previous list for a new comparison.