4,500 research outputs found
Vortex equations in abelian gauged sigma-models
We consider nonlinear gauged sigma-models with Kahler domain and target. For
a special choice of potential these models admit Bogomolny (or self-duality)
equations -- the so-called vortex equations. We find the moduli space and
energy spectrum of the solutions of these equations when the gauge group is a
torus T^n, the domain is compact, and the target is C^n or CP^n. We also obtain
a large family of solutions when the target is a compact Kahler toric manifold.Comment: v2: 60 pages, more details than in CMP versio
Non-transitive maps in phase synchronization
Concepts from the Ergodic Theory are used to describe the existence of
non-transitive maps in attractors of phase synchronous chaotic systems. It is
shown that for a class of phase-coherent systems, e.g. the sinusoidally forced
Chua's circuit and two coupled R{\"o}ssler oscillators, phase synchronization
implies that such maps exist. These ideas are also extended to other coupled
chaotic systems. In addition, a phase for a chaotic attractor is defined from
the tangent vector of the flow. Finally, it is discussed how these maps can be
used to real time detection of phase synchronization in experimental systems
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