arXiv subjects

Sofia B. S. D. Castro

Publications and source records attributed to Sofia B. S. D. Castro.

20 records · Page 2Linked to original sources

arXiv2014

Stability in simple heteroclinic networks in $\mathbb{R}^4$

We describe all heteroclinic networks in $\mathbb{R}^4$ made of simple heteroclinic cycles of types $B$ or $C$, with at least one common connecting trajectory. For networks made of cycles of type $B$, we study the stability of the cycles that make up the network as well as the stability of the network. We show that even when none of the cycles has strong stability properties the network as a whole may be quite stable. We prove, and provide illustrative examples of, the fact that the stability of the network does not depend {\em a priori} uniquely on the stability of the individual cycles.

math.DS↗

arXiv2012

The Discrete Markus-Yamabe Problem for Symmetric Planar Polynomial Maps

We probe deeper into the Discrete Markus-Yamabe Question for polynomial planar maps and into the normal form for those maps which answer this question in the affirmative. Furthermore, in a symmetric context, we show that the only nonlinear equivariant polynomial maps providing an affirmative answer to the Discrete Markus-Yamabe Question are those possessing Z2 as their group of symmetries. We use this to establish two new tools which give information about the spectrum of a planar polynomial map.

math.DS↗