Non-degeneracy conditions for plane branches

Beata Gryszka, Janusz Gwoździewicz

Let $x=t^n$, $y={\sum }_{i=1}^{\infty }{a}_i{t}^i$ be a parametrisation of the germ of a complex plane analytic curve $\Gamma$ at the origin. Then $\Gamma$ has the implicit equation $f(x,y)=0$ in th…