Descript 
108 p 
Note 
Source: Dissertation Abstracts International, Volume: 7207, Section: B, page: 4053 

Adviser: Jan Wehr 

Thesis (Ph.D.)The University of Arizona, 2011 

We study dynamical systems in the complex plane under the effect of constant noise. We show for a wide class of polynomial equations that the ergodic property is valid in the associated stochastic perturbation if and only if the noise added is in the direction transversal to all unstable trajectories of the deterministic system. This has the interpretation that noise in the "right" direction prevents the process from being unstable: a fundamental, but not wellunderstood, geometric principle which seems to underlie many other similar equations. In view of [Has80, JK85, Jur97, MT93b, RB06, SV72], the result is proven by using Lyapunov functions and geometric control theory 

School code: 0009 
Host Item 
Dissertation Abstracts International 7207B

Subject 
Applied Mathematics


Mathematics


Physics, Elementary Particles and High Energy


0364


0405


0798

Alt Author 
The University of Arizona. Mathematics

