相关论文: On the attractors of step skew products over the B…
In this paper, we establish homological mirror symmetry where the A-model is a finite quotient of the Milnor fibre of an invertible curve singularity, proving a conjecture of Lekili and Ueda from arXiv:1806.04345 in this dimension. Our…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older…
We study a class of skew products with overlaps in fibers and show that in this case the unstable manifolds really depend on prehistories, even for perturbations of the original maps. We also give several results about the Hausdorff…
We study skew product systems driven by a hyperbolic base map S (e.g. a baker map or an Anosov surface diffeomorphism) and with simple concave fibre maps on an interval [0,a] like h(x)=g(\theta) tanh(x) where g(\theta) is a factor driven by…
We develop a general geometric method to establish the existence of positive Lyapunov exponents for a class of skew products. The technique is applied to show non-uniform hyperbolicity of some conservative partially hyperbolic…
The main goal in this paper is to describe the geometric structure of invariant graphs of a certain class of skew products. Our focus is on attracting multi-graphs. An invariant multi-graph is an invariant compact set which is a finite…
In 2006, A. Gorodetski proved that central fibers of perturbed skew products are Holder continuous with respect to the base point. In the present paper we give an explicit estimate of the Holder exponent mentioned above. Moreover, we…
We study the dynamics of a superattracting skew product $f$ on the attracting basin. As the first strategy, we find out forward $f$-invariant wedge-shaped regions in the basin, on some of which $f$ is conjugate to monomial maps, and…
In this article, we develop a dynamical theory for what shall be called a skew product on the Berkovich projective line, $\phi_*: \mathbb{P}^1_{\text{an}}(K) \to \mathbb{P}^1_{\text{an}}(K)$ over a non-Archimedean field $K$. These functions…
In this paper we present new results about the topology of the Milnor fibrations of analytic function-germs with a special attention to the topology of the fibers. In particular, we provide a short review on the existence of the Milnor…
We discuss dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robust topologically mixing and for which almost all points in the same fiber…
This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The…
For any plane curve singularity defined by an analytic function germ $f$, we construct a spine on each Milnor fiber simultaneously, that realizes the vanishing topology. In order to do so, we study the separatrices at the origin of the…
In this note, we provide a quick introduction to the study of the Milnor fibration via the derived category and perverse sheaves. This is primarily a dictionary for translating from the standard topological setting to the derived category…
In this paper, a general construction of a skew product dynamical system, for which the skew product dynamical system studied by Hahn is a special case, is given. Then the ergodic and topological properties (of a special type) of our newly…
New results on the behaviour of the fast motion in slow-fast systems of ODEs with dependence on the fast time are given in terms of tracking of nonautonomous attractors. Under quite general assumptions, including the uniform ultimate…
The sandwiched surface singularities are those rational surface singularities which dominate birationally smooth surface singularities. de Jong and van Straten showed that one can reduce the study of the deformations of a sandwiched surface…
The existence of a global attractor is proved for the skew-product semiflow induced by almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which exponentially…
We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective system possesses a non-uniformly hyperbolic attractor. This is…