Topology in chaotic scattering

  title={Topology in chaotic scattering},
  author={David Sweet and Edward Ott and James A. Yorke},
In chaotic scattering, an initially freely moving orbit (such as that of an atom or a star) enters a scattering region and evolves chaotically for a period of time before it escapes and returns to free motion. We have looked at cases in which escape can occur in three or more distinct ways. Using a laboratory model, we demonstrate experimentally that the regions of state space (called basins) corresponding to different ways of escaping can have an interesting topological property that we call… 
Fractal and Wada Exit Basin Boundaries in tokamaks
This work describes an outer layer of chaotic magnetic field lines in a tokamak with an ergodic limiter by means of an analytical Poincare field line mapping and presents an involved fractal structure.
Basin topology in dissipative chaotic scattering.
A surprising finding is that, in the common case where multiple destinations exist for scattering trajectories, Wada basin boundaries are common and they appear to be structurally stable under weak dissipation, even when other characteristics of the nonhyperbolic scattering dynamics are not.
Testing for Basins of Wada
A simple algorithm whose purpose is to look for the Wada property in a given dynamical system is reported, which has the possibility to classify and study intermediate situations known as partially Wada boundaries.
New developments in classical chaotic scattering
This work provides a current overview of the field, where attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others.
Sources of uncertainty in deterministic dynamics: an informal overview
  • I. Stewart
  • Physics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2011
The main topics are the butterfly effect, uncertainty in initial conditions in non-chaotic systems, such as coin tossing, heteroclinic connections leading to apparently random switching between states, topological complexity of basin boundaries, bifurcations and collisions of chaotic attractors.
Escaping Dynamics in the Presence of Dissipation and Noise in Scattering Systems
This paper analyze the effects of adding external perturbations such as dissipation and noise in chaotic scattering phenomena and finds that a scaling law exists between the exponential decay rate of the particles and the dissipative parameter, and that the fractal dimension for the noisy case is the unity.


Chaotic scattering in the gravitational three-body problem.
It is found that the maps contain regular regions separated by rivers of chaotic behavior, and a new way of considering long-lived trajectories is presented, allowing long data sets to be qualitatively analyzed at a glance.
Basins of Attraction
Many remarkable properties related to chaos have been found in the dynamics of nonlinear physical systems. These properties are often seen in detailed computer studies, but it is almost always
Quantum-chaotic scattering effects in semiconductor microstructures.
A surprising failure is uncovered of the semiclassical diagonal-approximation theory in describing the magnitude of these quantum transport effects of classical chaotic scattering for semiconductor microstructures.