7,215 research outputs found

    Peeling Bifurcations of Toroidal Chaotic Attractors

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    Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review

    Connections of the Mesencephalic Locomotor Region (MLR) in the Cat

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    The cat entopeduncular nucleus (EN), which is the main output of the basal ganglia, is known to project to the mesencephalic tegmentum. We have been able to elicit antidromic responses in single EN neurons from the region of the mesencephalic locomotor region (MLR), then transect (precollicular-postmamillary) the brainstem and elicit rhythmic movements of the limbs by stimulation of the same site in the same animal. Injections of the fluorescent dye 2,4 diamidino phenylindole 2 HCL (DAPI) into this area induces retrograde labeling of cell bodies in EN and motor cortex. Injections of a tritiated amino acid (leucine) into the motor cortex induce terminal labeling in the area of the MLR. These studies describe convergent projections from EN and motor cortex to the MLR. These connections may be involved in the sequencing and ordering of voluntary movements in which locomotion is necessary

    Derivation of Source-Free Maxwell and Gravitational Radiation Equations by Group Theoretical Methods

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    We derive source-free Maxwell-like equations in flat spacetime for any helicity "j" by comparing the transformation properties of the 2(2j+1) states that carry the manifestly covariant representations of the inhomogeneous Lorentz group with the transformation properties of the two helicity "j" states that carry the irreducible representations of this group. The set of constraints so derived involves a pair of curl equations and a pair of divergence equations. These reduce to the free-field Maxwell equations for j=1 and the analogous equations coupling the gravito-electric and the gravito-magnetic fields for j=2.Comment: 15 pages, no figures, to appear in Int. J. Mod. Phys.
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