相关论文: Attracting basins of volume preserving automorphis…
Let F be an automorphism of C^k which has a fixed point. It is well known that the basin of attraction is biholomorphically equivalent to C^k. We will show that the basin of attraction of a sequence of automorphisms is also biholomorphic to…
We study whether the basin of attraction of a sequence of automorphisms of $\mathbb{C}^k$ is biholomorphic to $\mathbb{C}^k$. In particular we show that given any sequence of automorphisms with the same attracting fixed point, the basin is…
In this paper, we first construct $k$-dimensional compact complex manifolds from automorphisms of $\mathbb{C}^k$ which admit a fixed attracting point at infinity. Then, we charactize the fundamental group as well as the universal covering…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
The basin of attraction of a uniformly attracting sequence of holomorphic automorphisms that agree to a certain order in the common fixed point, is biholomorphic to $\mathbb{C}^n$. We also give sufficient estimates how large this order has…
The purpose of this paper is to present several examples of non--autonomous basins of attraction that arise from sequences of automorphisms of $\mathbb C^k$. In the first part, we prove that the non-autonomous basin of attraction arising…
Let $X$ be a Stein manifold of dimension $n\geq 2$ satisfying the volume density property with respect to an exact holomorphic volume form. For example, $X$ could be $\mathbb{C}^n$, any connected linear algebraic group that is not…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be…
We establish two results under which the topology of a hyperbolic set constrains ambient dynamics. First if a set is a compact, transitive, expanding hyperbolic attractor of codimension 1 for some diffeomorphism, then it is a union of…
We study generic volume-preserving diffeomorphisms on compact manifolds. We show that the following property holds generically in the $C^1$ topology: Either there is at least one zero Lyapunov exponent at almost every point, or the set of…
Consider a holomorphic automorphism which acts hyperbolically on some invariant compact set. Then for every point in the compact set there exists a stable manifold, which is a complex manifold diffeomorphic to real Euclidean space. If the…
In this paper we shall give examples of maps and automorphisms with regions of attraction that are not simply connected.
We study basins of attraction of automorphisms of $\CC^2$ tangent to the identity that fix both axes. Our main result is that, if a well known conjecture about automorphisms of $\CC^*\times\CC^*$ holds, then there are no basins of…
We study the dynamics of generic volume-preserving automorphisms $f$ of a Stein manifold $X$ of dimension at least 2 with the volume density property. Among such $X$ are all connected linear algebraic groups (except $\mathbb{C}$ and…
We study the fixed point sets of holomorphic self-maps of a bounded domain in ${\Bbb C}^n$. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be…
A fixed point theorem is proved for inverse transducers, leading to an automata-theoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is…
Consider a holomorphic automorphism acting hyperbolically on an invariant compact set. It has been conjectured that the arising stable manifolds are all biholomorphic to Euclidean space. Such a stable manifold is always equivalent to the…
We consider both hyperbolic sets and partially hyperbolic sets attracting a set of points with positive volume in a Riemannian manifold. We obtain several results on the topological structure of such sets for diffeomorphisms whose…
The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface attractors and repellers. The main results of the paper relate…