arXiv subjects

Renato B. Bortolatto

Publications and source records attributed to Renato B. Bortolatto.

2 recordsLinked to original sources

arXiv2014

A note on the Liénard-Chipart criterion and roots of some families of polynomials

We present some inequalities that provide different sufficient conditions for an univariate monic polynomial to be Hurwitz unstable. These are motivated by difficult control problems where direct application of the Liénard-Chipart criterion is not feasible. Hurwitz stability of some polynomials of degree five is also discussed. These results may be interpreted as stability results for some interval polynomials.

math.DS↗

arXiv2012

Ergodicity and annular homeomorphisms of the torus

Let $f: \mathbb{T}^2 \to \mathbb{T}^2$ be a homeomorphism homotopic to the identity and $F: \mathbb{R}^2 \to \mathbb{R}^2$ a lift of $f$ such that the rotation set $ρ(F)$ is a line segment of rational slope containing a point in $\mathbb{Q}^2$. We prove that if $f$ is ergodic with respect to the Lebesgue measure on the torus and the average rotation vector (with respect to same measure) does not belong to $\mathbb{Q}^2$ then some power of $f$ is an annular homeomorphism.

math.DS↗