Originally introduced in 1974 by O.E. Rössler, the Rössler system is one of the most famous examples of chaotic flows, being generated by a stretch-and-fold mechanism. Despite being (arguably) the least non-linear flow one can think of, the Rössler system is known to be rich in nonlinear phenomena - for example: spiral homoclinic bifurcations, stability windows and period-doubling routes to chaos to name a few. In this talk we state and prove a topological criterion for the existence of complex dynamics for the Rössler system, which include infinitely many periodic trajectories. Time permitting, we will characterize the topology of these periodic trajectories, prove their persistence under perturbations - as well as discuss their possible bifurcations and how it all relates to the well-known Rössler attractor. 

מנחה: ד"ר טלי פינסקי