动力系统

Joinings are fundamental global objects in ergodic theory, yet in compact metric models one naturally observes only finite orbit-distance patterns. We bridge this gap by introducing multi-particle distance arrays, which sample finite orbit…

We prove that dichotomies given by growth rates that are either faster or slower than exponential either do not occur or are inconsequential in the setting of skew-products with compact base. A similar conclusion is obtained for the…

A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…

Let $p_1,...,p_L\in Z[x_1,...,x_d]$ be non-constant polynomials with zero constant term. The ergodic theoretical proofs of the polynomial and the IP-polynomial Szemeredi theorems as well as some of the ergodic-theoretical and combinatorial…

We show that the conditional survival probability measure for a Sinai billiard with a small hole on the boundary of the table is differentiable with respect to the size t of the hole at t = 0 and we compute the derivative.

We investigate the effect of a Heaviside cut-off on the front propagation dynamics of the so-called Burgers-FisherKolmogoroff-Petrowskii-Piscounov (Burgers-FKPP) advection-reaction-diffusion equation. We prove the existence and uniqueness…

Every transitive cellular automaton (CA) is sensitive to initial conditions. We study this implication in the more general context of non-uniform cellular automata (NUCA) with finitely many different local update rules assigned to cells. We…

Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…

We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$, where $g$ is of the form $af^p + b$ with $a,b \in \C$, $p \in \N$, and $a \neq 0,1$. We establish that the escaping sets, filled Julia sets, and…

This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable,…

We study the Lawn Mowing Problem restricted to periodic billiard paths in the unit square. Given the combinatorial data of a trajectory, we determine the optimal covering radius, and identify the shortest path that covers the square for any…

We show that every $C^2$ minimal action of Thompson group $T$ on the circle is ergodic with respect to the Lebesgue measure. If such action is not minimal then the Lebesgue measure of the exceptional minimal set is zero.

This paper investigates the chaotic properties of Arnol'd cat maps (ACMs) coupled on the nodes of a circulant graph. By demanding that the system's evolution matrix be symplectic, we determine the coupling matrix, which is naturally…

In this manuscript, we introduce a family of parametrized non-homogeneous linear complex differential equations on $[1,\infty)$, depending on a complex parameter. We identify a "Rotation number hypothesis" on the non-homogeneous term, which…

We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…

In this manuscript, we show that the Riemann zeta function satisfies $\big(\zeta(s),\zeta(1-\overline{s})\big)\neq(0,0)$ for any $s$ in the critical strip, except on the critical line. This still holds even when the fractional part function…

We consider the integrable dynamics of a Kepler billiard in the plane bounded by a branch of a conic section focused at the Kepler center. We show that in this case, for non-zero-energy orbits, the lines of consecutive second orbital foci…

We study the geometry of reflection of a massive point-like particle at conic section boundaries. Thereby the particle is subjected to a central force associated with either a Kepler or Hooke potential. The conic section is assumed to have…

With the dual variational principle and the saddle point reduction we use the abstract bifurcation theory recently developed by author in previous work to prove many new bifurcation results for solutions of four types of Hamiltonian…