English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This article treats chaotic scattering with three degrees of freedom, whereone of them is open and the other two are closed, as a first step toward a moregeneral understanding of chaotic scattering in higher dimensions.  Despite of the strong restrictions it breaks the essential simplicityimplicit in any two-dimensional time-independent scattering problem.Introducing the third degree of freedom by breaking a continuous symmetry, wefirst explore the topological structure of the homoclinic/heteroclinic tangleand the structures in the scattering functions. Then we work out implicationsof these structures for the doubly differential cross section. The mostprominent structures in the cross section are rainbow singularities. They forma fractal pattern which reflects the fractal structure of the chaotic invariantset. This allows to determine structures in the cross section from theinvariant set and conversely, to obtain information about the topology of theinvariant set from the cross section. The latter is a contribution to theinverse scattering problem for chaotic systems.

The chaotic set and the cross section for chaotic scattering beyond in 3 degrees of freedom