Scattering off two oscillating disks: Dilute chaos

Papachristou, PK; Diakonos, FK; Constantoudis, V; Schmelcher, P; Benet, L

dc.contributor.author	Papachristou, PK	en
dc.contributor.author	Diakonos, FK	en
dc.contributor.author	Constantoudis, V	en
dc.contributor.author	Schmelcher, P	en
dc.contributor.author	Benet, L	en
dc.date.accessioned	2014-03-01T01:21:19Z
dc.date.available	2014-03-01T01:21:19Z
dc.date.issued	2004	en
dc.identifier.issn	1063-651X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16203
dc.subject.classification	Physics, Fluids & Plasmas	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.other	Dynamics	en
dc.subject.other	Functions	en
dc.subject.other	Hamiltonians	en
dc.subject.other	Oscillations	en
dc.subject.other	Phase measurement	en
dc.subject.other	Scattering	en
dc.subject.other	One dimensional scattering	en
dc.subject.other	Oscillating disks	en
dc.subject.other	Two-dimensional scattering systems	en
dc.subject.other	Unstable periodic orbits (UPO)	en
dc.subject.other	Chaos theory	en
dc.title	Scattering off two oscillating disks: Dilute chaos	en
heal.type	journalArticle	en
heal.identifier.primary	10.1103/PhysRevE.70.056215	en
heal.identifier.secondary	http://dx.doi.org/10.1103/PhysRevE.70.056215	en
heal.identifier.secondary	056215	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	We investigate the role of the unstable periodic orbits and their manifolds in the dynamics of a time-dependent two-dimensional scattering system. As a prototype we use two oscillating disks on the plane with the oscillation axes forming an angle theta. The phase space of the system is five dimensional and it possesses a variety of families of unstable periodic orbits (UPOs) with intersecting manifolds. We perform numerical experiments to probe the structure of distinct scattering functions, in one and two dimensions, near the location of the UPOs. We find that the corresponding manifolds occur only in a very particular and localized way in the high-dimensional phase space. As a consequence the underlying fractal structure is ubiquitous only in higher-dimensional, e.g., two-dimensional, scattering functions. Both two-dimensional and one-dimensional scattering functions are dominated by seemingly infinite sequences of discontinuities characterized by small values of the magnitude of the projectile's outgoing velocity. These peaks accumulate toward the phase-space locations of the UPOs, with a rate which monotonically depends on the corresponding instability exponent. They represent the intersections of the set of the initial conditions with invariant sets of larger dimensionality embedded in the phase space of the system, which are not directly related with the UPOs. We adopt the term "dilute chaos" to characterize these phenomenological aspects of the scattering dynamics.	en
heal.publisher	AMERICAN PHYSICAL SOC	en
heal.journalName	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics	en
dc.identifier.doi	10.1103/PhysRevE.70.056215	en
dc.identifier.isi	ISI:000225970700063	en
dc.identifier.volume	70	en
dc.identifier.issue	5 2	en
dc.identifier.spage	056215	en
dc.identifier.epage	1-056215-18	en