动力系统

We study cocycles taking values in the mapping class group of closed surfaces and investigate their leading topological Lyapunov exponent. Under a natural closing property, we show that the top topological Lyapunov exponent can be…

We study the global (asymptotic) stability of the Lengyel-Epstein differential systems, sometimes called Belousov-Zhabotinsky differential systems. Such systems are topologically equivalent to a two-parameter family of cubic systems in the…

We introduce and study a unital version of shift equivalence for finite square matrices over the nonnegative integers. In contrast to the classical case, we show that unital shift equivalence does not coincide with one-sided eventual…

This paper is concerned with the Lyapunov spectrum for measurable cocycles over an ergodic pmp system taking values in semi-simple real Lie groups. We prove simplicity of the Lyapunov spectrum and its continuity under certain perturbations…

If $f:\mathbb{R}^2\rightarrow \mathbb{R}^2$ is an orientation reversing fixed point free homeomorphism on the plane $\mathbb{R}^2$ with no unbounded orbit, then $f$ has infinitely many periodic orbits.

This paper investigates the dynamics of the Nicholson's blowffies equation with stage structure and harvest. By employing the property of Lambert W function, the existence of positive equilibria is obtained. With aid of the distribution of…

Let Aff(X) be the group of affine diffeomorphisms of a closed homogeneous manifold X=G/B admitting a G-invariant Lebesgue-Haar probability measure $\mu$. For $f_0\in$ Aff(X), let $Z^\infty(f_0)$ be the group of $C^\infty$ diffeomorphisms of…

In recent years, the study on the impact of competition on additional food provided prey-predator systems have gained significant attention from researchers in the field of mathematical biology. In this study, we consider an additional food…

Motivated by the study of billiards in polyhedra, we study linear flows in a family of singular flat $3$-manifolds which we call translation prisms. Using ideas of Furstenberg and Veech, we connect results about weak mixing properties of…

We prove that for $\mathcal{C}^{1,\alpha}$ diffeomorphisms on a compact manifold $M$ with ${\rm dim} M\leq 3$, if an invariant measure $\mu$ is a continuity point of the sum of positive Lyapunov exponents, then $\mu$ is an upper…

Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic…

We investigate dimension-theoretic properties of concentric topological spheres, which are fractal sets emerging both in pure and applied mathematics. We calculate the box dimension and Assouad spectrum of such collections, and use them to…

This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of…

We obtain expansions of ergodic integrals for $\Z^d$-covers of compact self-similar translation flows, and as a consequence we obtain a form of weak rational ergodicity with optimal rates. As examples, we consider the so-called self-similar…

We show that every infinite, locally finite, and connected graph admitsa translation-like action by $\mathbb{Z}$, and that this action can be takento be transitive exactly when the graph has either one or two ends.The actions constructed…

We show that a central limit theorem holds for exterior powers of the Kontsevich-Zorich (KZ) cocycle. In particular, we show that, under the hypothesis that the top Lyapunov exponent on the exterior power is simple, a central limit theorem…

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

Let Q be a component of a stratum of abelian or quadratic differentials on an oriented surface of genus $g\geq 0$ with $m\geq 0$ punctures and $3g-3+m\geq 2$. We construct a subshift of finite type $(\Omega,\sigma)$ and a Borel suspension…

Let $(G,+)$ be a countable abelian group such that the subgroup $\{g+g\colon g\in G\}$ has finite index and the doubling map $g\mapsto g+g$ has finite kernel. We establish lower bounds on the upper density of a set $A\subset G$ with respect…

We give a construction of a smooth realization of a pseudo-Anosov diffeomorphism of a Riemannian surface, and show that it admits a unique SRB measure with polynomial decay of correlations, large deviations, and the central limit theorem.…