Open AccessSingular hyperbolic systems
Author(s) -
C. A. Morales,
María José Pacífico,
Enrique Pujals
Publication year - 1999
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-99-04936-9
Subject(s) - lorenz system , attractor , gravitational singularity , mathematics , class (philosophy) , mathematical analysis , vector field , pure mathematics , geometry , computer science , artificial intelligence
We construct a class of vector fields on 3-manifolds containing the hyperbolic ones and the geometric Lorenz attractor. Conversely, we shall prove that nonhyperbolic systems in this class resemble the Lorenz attractor: they have Lorenz-like singularities accumulated by periodic orbits and they cannot be approximated by flows with nonhyperbolic critical elements.