General properties of maps associated with systems in which trajectories of the flow get close to a hyperbolic fixed point with a two-dimensional stable and a one-dimensional unstable manifold are examined in the chaotic region. Exponents characterizing power law singular behaviour of the Jacobian, of the shape of and of the stationary probability distribution on the chaotic attractor are expressed in terms of the ratios of the eigenvalues of the linearized flow at the hyperbolic point. Emphasis is laid on the study of the limiting case of strong dissipation leading to a simple one-dimensional attractor but to a dynamics with interesting features.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics