$\mathbf{Definition:}$ Let $ X,Y $ be two metric spaces and $ f:X\to X$ and $g:Y \to Y$ be two mappings, $f $ and $g$ are said to be Topollogically Conjugated (denoted by $f\sim g$) if there exist $h:X\to Y$ homeomorphism s.t $h\circ f = g\circ h$
$\mathbf{Question:}$ I am given with two mappings, $f$ and $g$, both from $\Bbb T^2 \to \Bbb T^2$, s.t $$f\begin{pmatrix}x\\y\\\end{pmatrix} = \begin{pmatrix}2&1\\1&1\\\end{pmatrix}\begin{pmatrix}x\\y\\\end{pmatrix} + \begin{pmatrix}a\\b\\\end{pmatrix}$$ Where $a,b\in \Bbb R$. And the second is "Arnold's cat map" given as $$g\begin{pmatrix}x\\y\\\end{pmatrix} = \begin{pmatrix}2&1\\1&1\\\end{pmatrix}\begin{pmatrix}x\\y\\\end{pmatrix}$$ And I have asked to prove $f\sim g$. I tried a lot, but I didn't succeeded. Please if any one help me regarding finding that homeomorphism '$h$'. Thanks