2 results
Topological and geometric hyperbolicity criteria for polynomial automorphisms of
${\mathbb {C}^2}$
- Part of
-
- Journal:
- Ergodic Theory and Dynamical Systems / Volume 42 / Issue 7 / July 2022
- Published online by Cambridge University Press:
- 04 May 2021, pp. 2151-2171
- Print publication:
- July 2022
-
- Article
-
- You have access
- Open access
- Export citation
-
We prove that uniform hyperbolicity is invariant under topological conjugacy for dissipative polynomial automorphisms of
$\mathbb {C}^2$
. Along the way we also show that a sufficient condition for hyperbolicity is that local stable and unstable manifolds of saddle points have uniform geometry.
A Note on Locally Nilpotent Derivations and Variables of k[X, Y, Z]
-
- Journal:
- Canadian Mathematical Bulletin / Volume 52 / Issue 4 / 01 December 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 535-543
- Print publication:
- 01 December 2009
-
- Article
-
- You have access
- Export citation
-
We strengthen certain results concerning actions of
$\left( \mathbb{C},\,+ \right)$ on 
${{\mathbb{C}}^{3}}$ and embeddings of 
${{\mathbb{C}}^{2}}$ in ${{\mathbb{C}}^{3}}$, and show that these results are in fact valid over any field of characteristic zero.
