动力系统

In this paper, we study certain dynamical properties of dill maps, a class of functions introduced in~\cite{salo2015block} that generalizes both cellular automata and substitutions. In particular, we prove that surjective uniform dill maps…

The Kalman(-Bucy) filter is the natural choice for the state reconstruction of disturbed, linear dynamical systems based on flawed and incomplete measurements. Taking a deterministic viewpoint this work investigates possible extensions of…

We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic,…

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…

Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…

The goal of this paper is to provide a methodology to prove existence of (fiberwise hyperbolic) real-analytic invariant tori in real-analytic quasi-periodic skew-product dynamical systems that present nearly-invariant tori of the same…

We consider an area-preserving diffeomorphism of a compact surface, which is assumed to be an irrational rotation near each boundary component. A finite set of periodic orbits of the diffeomorphism gives rise to a braid in the mapping…

We investigate the structure of transversely K\"ahler foliations with quasi-negative tranverse Ricci curvature. In particular, we prove a de Rham type theorem decomposition on the leaf space where we characterize each factor.

For a hyperbolic rational map $f$ with connected Julia set, we give upper and lower bounds on the Ahlfors-regular conformal dimension of its Julia set $J_f$ from a family of energies of associated graph maps. Concretely, the dynamics of $f$…

We study bifurcations of vector fields on 2-manifolds with handles in generic one-parameter families unfolding vector fields with a separatrix loop of a hyperbolic saddle. These bifurcations can differ drastically from the analogous…

This paper is concerned with some stronger forms of transitivity in non-autonomous discrete systems$(f_{ 1,\infty})$ generated by a uniformly convergent sequence of continuous self maps. Firstly, we present two counterexamples to show that…

In this paper, we define the so-called square entropy and prove that n-to-1 full zip shift maps are intrinsically ergodic. Furthermore, we show that square entropy characterizes uniform n-to-1 transformations of $(m,l)$-Bernoulli type that…

We prove that an Anosov action of $\mathbb{R}^k$ over a compact manifold $M$ transitive on regular sub-cones satisfies the dichotomy: each stable and unstable leaf is dense or the Anosov action is topologically conjugated to a suspension of…

The double Hamiltonian Hopf bifurcation is studied, i.e. a generic two-parametric unfolding of a smooth Hamiltonian system with four degrees of freedom which has at the critical value of parameters the equilibrium with two pairs of double…

It is known that all uniformly expanding dynamics $f: M \rightarrow M$ have no phase transition with respect to a H\"older continuous potential $\phi : M \rightarrow \mathbb{R}$, in other words, the topological pressure function $\mathbb{R}…

We consider a random dynamical system on $\mathbb{R}^d$, whose dynamics is defined by a stochastic differential equation. The annealed transfer operator associated with such systems is a kernel operator. Given a set of feasible…

We develop a powerful and general method to provide rigorous and accurate upper and lower bounds for Lyapunov exponents of stochastic flows. Our approach is based on computer-assisted tools, the adjoint method and established results on the…

We prove that every transitive topologically Anosov flow on a closed 3-manifold is orbitally equivalent to a smooth Anosov flow, preserving an ergodic smooth volume form.

The goal of these notes is to make the concept of "pseudo goodwin cycles" mathematically more precise. At first the title seems like a contradiction to have a wage-led model and still find goodwin cycles in it, but the point we try to make…

A CR-dynamical system is a pair $(X, G)$, where $X$ is a non-empty compact Hausdorff space with uniformity $\mathscr{U}$ and $G$ is a closed relation on $X$. In this paper we introduce the $(i, j)$-shadowing properties in CR-dynamical…