Federico Juan Rodriguez Hertz, Dissertation Advisor/Co-Advisor Federico Juan Rodriguez Hertz, Committee Chair/Co-Chair Boris V Kalinin, Committee Member Zhiren Wang, Committee Member Eugenio Bianchi, Outside Member
Keywords:
dynamical systems rank 1 factors abelian actions rigidity
Abstract:
Given the linear endomorphisms $A=\left(\begin{array}{cc}
2&0\\
0& 2
\end{array}\right)$ and $B=\left(\begin{array}{cc}
1&1\\
0& 1
\end{array}\right)$ on $\T^2$ and commuting perturbations $f$ of $A$ and $g$ of $B$, we build a simultaneous smooth conjugacy between $(f,g)$ and $(\hat A,B)$ where $\hat A(x,y)=(2x+\beta(y),2y)$ for some smooth $\beta:\T^2\to\R$. This shows rigidity of commuting maps with rank 1 factors beyond what was expected.
