Solar storms, cycles and topology

Solar storms are produced due to plasma processes inside and between coronal loops. These loops are topologically examined using knot and braid theory. Solar cycles are topologically explored with a complex generalization of the three ordinary differential equations studied by Lorenz. By studying the Poincaré map we give numerical evidence that the flow has an attractor with fractal structure. The period is defined as the time needed for a point on a hyperplane to return to the hyperplane again. The periods are distributed in an interval. For large values of the Dynamo number there is a long tail toward long periods and other interesting comet-like features. We also found a relationship between the intensity of a cycle and the length for the previous cycle. Maunder like minima are also appearing. These general relations found for periods can further be physically interpreted with improved helioseismic estimates of the parameters used by the dynamical systems. Solar Dynamic Observatory is expected to offer such improved measurements.