Related papers: Remarks on Automorphisms of $\mathbb{C}^* \times \…
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…
We prove the existence of a compact random attractor for the stochastic Benjamin-Bona-Mahony Equation defined on an unbounded domain. This random attractor is invariant and attracts every pulled-back tempered random set under the forward…
The goal of this paper is to study the dynamics of holomorphic diffeomorphisms in C^n such that the resonances among the first 1<= r<= n eigenvalues of the differential are generated over N by a finite number of Q-linearly independent…
A basic problem in complex dynamics is to understand orbits of holomorphic maps. One problem is to understand the collection of points $S$ in an attracting basin whose forward orbits land exactly on the attracting fixed point. In the paper…
We consider AF-flows, i.e., one-parameter automorphism groups of a unital simple C*-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence…
We study the existence of universal autohomeomorphisms of $\mathbb{N}^*$. We prove that $\mathsf{CH}$ implies there is such an autohomeomorphism and show that there are none in any model where all autohomeomorphisms of $\mathbb{N}^*$ are…
In this paper, we study geometric properties of basins of attraction of monotone systems. Our results are based on a combination of monotone systems theory and spectral operator theory. We exploit the framework of the Koopman operator,…
We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors), in the planar circular restricted five-body problem (CR5BP). The evolution of the position and the linear stability…
It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using…
We provide several new examples in dynamics on the $2$-sphere, with the emphasis on better understanding the induced boundary dynamics of invariant domains in parametrized families. First, motivated by a topological version of the…
We study discrete fixed point sets of holomorphic self-maps of complex manifolds. The main attention is focused on the cardinality of this set and its configuration. As a consequence of one of our observations, a bounded domain in ${\Bbb…
For unital $C^*$-algebras $A$ and $B$, we completely characterize the isometric ($*$-) automorphisms of their Banach space projective tensor product $A\otimes^\gamma B$. This leads to the characterization of inner and outer isometric…
The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation…
We construct transcendental automorphims of $\mathbb{C}^{2}$ having an unbounded and regular Siegel domain.
This paper investigates the Brennan Conjecture for domains $\Omega$ that arise as basins of attraction of a polynomial. We extend the result of Baranski, Volberg, and Zdunik to a broader class of polynomials. We prove that for any monic…
A point x is a (bow) tie-point of a space X if X setminus {x} can be partitioned into (relatively) clopen sets each with x in its closure. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of betaN setminus N=…
Araujo proved in his thesis \cite{A} that a $C^1$ generic surface diffeomorphism has either infinitely many sinks (i.e. attracting periodic orbits) or finitely many hyperbolic attractors with full Lebesgue measure basin. The goal of this…
We prove that the set of diffeomorphisms having at most finitely many attractors contains a dense and open subset of the space of $C^1$ partially hyperbolic diffeomorphisms with one-dimensional center. This is obtained thanks to a robust…
We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors of the convergence process), in the generalized H\'{e}non-Heiles system (GHH). The evolution of the position as well…
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…