Abstract
A chaotic attractor solution of the Lorenz system [Lorenz, 1963] with foliated structure is topologically characterized. Its template permits to both summarize the organization of its periodic orbits and detail the topology of the solution as a branched manifold. A template of an attractor solution of the Chen system [Chen & Ueta, 1999] with a similar foliated structure is also established.
Highlights
The Lorenz system has been introduced with a set of parameters [1] for which the solution is a chaotic attractor
The topology of this solution has been established by Birman & Williams [3] considering the periodic orbits of the solution as knots evolving in a branched manifold, currently called template
This topological analysis of a chaotic attractor permits to obtain a template that synthesises the relative organisation of its periodic orbits
Summary
Templates of Two Foliated Attractors - Lorenz and Chen Systems. International journal of bifurcation and chaos in applied sciences and engineering , World Scientific Publishing, 2016, 26 (02), pp.1650037. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
