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res:
bibo_abstract:
- Systems such as fluid flows in channels and pipes or the complex Ginzburg–Landau
system, defined over periodic domains, exhibit both continuous symmetries, translational
and rotational, as well as discrete symmetries under spatial reflections or complex
conjugation. The simplest, and very common symmetry of this type is the equivariance
of the defining equations under the orthogonal group O(2). We formulate a novel
symmetry reduction scheme for such systems by combining the method of slices with
invariant polynomial methods, and show how it works by applying it to the Kuramoto–Sivashinsky
system in one spatial dimension. As an example, we track a relative periodic orbit
through a sequence of bifurcations to the onset of chaos. Within the symmetry-reduced
state space we are able to compute and visualize the unstable manifolds of relative
periodic orbits, their torus bifurcations, a transition to chaos via torus breakdown,
and heteroclinic connections between various relative periodic orbits. It would
be very hard to carry through such analysis in the full state space, without a
symmetry reduction such as the one we present here.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Nazmi B
foaf_name: Budanur, Nazmi B
foaf_surname: Budanur
foaf_workInfoHomepage: http://www.librecat.org/personId=3EA1010E-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-0423-5010
- foaf_Person:
foaf_givenName: Predrag
foaf_name: Cvitanović, Predrag
foaf_surname: Cvitanović
bibo_doi: 10.1007/s10955-016-1672-z
bibo_issue: 3-4
bibo_volume: 167
dct_date: 2017^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Unstable manifolds of relative periodic orbits in the symmetry reduced
state space of the Kuramoto–Sivashinsky system@
...