We show that transverse perturbations from structurally stable heteroclinic cycles can be destabilized by surprisingly small amounts of noise, even when each individual fixed point of the cycle is stable to transverse modes. A condition that favours this process is that the linearization of the dynamics in the transverse direction be characterized by a non-normal matrix. The phenomenon is illus...

This paper is concerned with the existence of mild solution for impulsive stochastic differential equations with nonlocal conditions in PC -norm. Our approach is based on Krasnoselskii fixed point theorem. Mathematics subject classification (2010): 34K50, 60H15.

The world does not need yet another proof of the classical no retraction theorem (NRT) and its equivalent partner the Brouwer fixed point theorem (BFPT)— many lovely elementary proofs are widely known. What does merit a new proof, however, is a much less well-known generalization of the NRT to a broader class of topological spaces than only those that are homeomorphic to balls (which is what th...

We use quantum field theory methods to study the network model for the spin quantum Hall transition. When the couplings are fine tuned in a certain way, the spin and charge degrees of freedom, corresponding to the supercurrent algebras su(2)0 and osp(2|2)−2 respectively, decouple in the renormalization group flow. The infrared fixed point of this simpler theory is the coset osp(4|4)1/su(2)0 whi...

We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to 2e2/h and vanishing thermal Hall conductivity. In contrast to the integer quantum Hall state of fermions, a point contact can have a dramatic effect on the low-energy physics. In the absence of disorder, a point contact generically lea...

We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to 2e/h and vanishing thermal Hall conductivity. In contrast to the integer quantum Hall state of fermions, a point contact can have a dramatic effect on the low energy physics. In the absence of disorder, a point-contact generically lead...