85 citations · 175 across the 25 of their papers we have counts for
27 papers
Intermingled basins: Kan's example on the Riemann sphere
Abbas Fakhari, Ale Jan Homburg, Sebastian van Strien
Kan's discovery of dynamical systems with two attractors whose basins of attraction both have full support, featured specific examples of skew product systems of interval diffeomor…
Robust reconstruction of sparse network dynamics
Tiago Pereira, Edmilson Roque dos Santos, Sebastian van Strien
Reconstruction of the network interaction structure from multivariate time series is an important problem in multiple fields of science. This problem is ill-posed for large network…
Holomorphic motions, natural families of entire maps, and multiplier-like objects for wandering domains
Gustavo R. Ferreira, Sebastian van Strien
Structural stability of holomorphic functions has been the subject of much research in the last fifty years. Due to various technicalities, however, most of that work has focused o…
Dennis Sullivan's Work on Dynamics
Edson de Faria, Sebastian van Strien
In this expository paper, we provide the readers with an overview of Dennis Sullivan's major contributions to the area of Dynamical Systems.
Conjugacy classes of real analytic one-dimensional maps are analytic connected manifolds
Trevor Clark, Sebastian van Strien
An important question is to describe topological conjugacy classes of dynamical systems. Here we show that within the space of real analytic one-dimensional maps with critical poin…
The dynamics of complex box mappings
Trevor Clark, Kostiantyn Drach, Oleg Kozlovski +1
In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the retur…
Positive Transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps
Genadi Levin, Weixiao Shen, Sebastian van Strien
In this paper we will develop a general approach which shows that generalized "critical relations" of families of locally defined holomorphic maps on the complex plane unfold trans…
Transversality in the setting of hyperbolic and parabolic maps
Genadi Levin, Weixiao Shen, Sebastian van Strien
In this paper we consider families of holomorphic maps defined on subsets of the complex plane, and show that the technique developed in \cite{LSvS1} to treat unfolding of critical…
Heterogeneously Coupled Maps: hub dynamics and emergence across connectivity layers
Tiago Pereira, Sebastian van Strien, Matteo Tanzi
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called…
Transversality for critical relations of families of rational maps: an elementary proof
Genadi Levin, Weixiao Shen, Sebastian van Strien
In this paper we will give a short and elementary proof that critical relations unfold transversally in the space of rational maps.
Monotonicity of entropy and positively oriented transversality for families of interval maps
Genadi Levin, Weixiao Shen, Sebastian van Strien
In this paper we will develop a very general approach which shows that critical relations of holomorphic maps on the complex plane unfold transversally in a positively oriented way…
Robustness of ergodic properties of nonautonomous piecewise expanding maps
Matteo Tanzi, Tiago Pereira, Sebastian van Strien
Recently, there has been an increasing interest on nonautonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map results in stati…
On 2-diffeomorphisms with one-dimensional basic sets and a finite number of moduli
V. Z. Grines, O. V. Pochinka, S. Van Strien
This paper is a step towards the complete topological classification of Ω-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions…
Dynamics of Coupled Maps in Heterogeneous Random Networks
Tiago Pereira, Sebastian van Strien, Jeroen S. W. Lamb
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes…
Payoff Performance of Fictitious Play
Georg Ostrovski, Sebastian van Strien
We investigate how well continuous-time fictitious play in two-player games performs in terms of average payoff, particularly compared to Nash equilibrium payoff. We show that in m…
On stochastic stability of expanding circle maps with neutral fixed points
Weixiao Shen, Sebastian van Strien
It is well-known that the Manneville-Pomeau map with a parabolic fixed point of the form is stochastically stable for and the limiting measure…
Piecewise Linear Hamiltonian Flows Associated to Zero-Sum Games: Transition Combinatorics and Questions on Ergodicity
Georg Ostrovski, Sebastian van Strien
In this paper we consider a class of piecewise affine Hamiltonian vector fields whose orbits are piecewise straight lines. We give a first classification result of such systems and…
Density of hyperbolicity for classes of real transcendental entire functions and circle maps
Lasse Rempe-Gillen, Sebastian van Strien
We prove density of hyperbolicity in spaces of (i) real transcendental entire functions, bounded on the real line, whose singular set is finite and real and (ii) transcendental sel…
One-Parameter Families of Smooth Interval Maps: Density of Hyperbolicity and Robust Chaos
Sebastian van Strien
In this note we will discuss the notion of robust chaos, and show that (i) there are natural one-parameter families with robust chaos and (ii) hyperbolicity is dense within generic…
A new class of Hamiltonian flows with random-walk behavior originating from zero-sum games and Fictitious Play
S van Strien
In this paper we relate dynamics associated to zero-sum games (Fictitious play) to Hamiltonian dynamics. It turns out that the Hamiltonian dynamics which is induced from fictitious…
Monotonicity of entropy for real multimodal maps
Henk Bruin, Sebastian van Strien
In \cite{Mil}, Milnor posed the {\em Monotonicity Conjecture} that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entr…
Rational functions with real multipliers
Alexandre Eremenko, Sebastian van Strien
Let f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this…
Absence of line fields and Mane's theorem for non-recurrent transcendental functions
Lasse Rempe, Sebastian van Strien
Let f be a transcendental meromorphic function. Suppose that the finite part of the postsingular set of f is bounded, that f has no recurrent critical points or wandering domains,…
Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials
Oleg Kozlovski, Sebastian van Strien
We prove that topologically conjugate non-renormalizable polynomials are quasi-conformally conjugate. From this we derive that each such polynomial can be approximated by a hyperbo…