3 papers
math.DS2025
Polynomial skew products with small relative degree
Romain Dujardin, Charles Favre, Matteo Ruggiero
We investigate the local dynamics of a proper superattracting holomorphic germ in possessing a totally invariant line such that with $d\ge 2…
math.DS2023
On the dynamical Manin-Mumford conjecture for plane polynomial maps
Romain Dujardin, Charles Favre, Matteo Ruggiero
We prove the dynamical Manin-Mumford conjecture for regular polynomial maps of A^2 and irreducible curves avoiding super-attracting orbits at infinity, over any field of characteri…
math.DS2014
A two-dimensional polynomial mapping with a wandering Fatou component
Matthieu Astorg, Xavier Buff, Romain Dujardin +2
We show that there exist polynomial endomorphisms of C^2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorph…