动力系统

Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau…

We show that if $(X, \mu, T)$ is a probability measure-preserving dynamical system, and $\mathscr{P}$ is a countable partition of $(X, \mu)$, then the limit $$ \lim_{n, k \to \infty} \mathbb{E} \left[ \frac{1}{k} \sum_{j = 0}^{k - 1} f…

We consider interval maps with countably many full branches and observables with polynomial tails. We show that the Birkhoff spectrum is real analytic and that its convergence to the Hausdorff dimension of the repeller is governed by the…

Various line fields naturally arise on surfaces in both physical and biological contexts, and generic singularities frequently appear in the form of 1-prong (thorn-like) and 3-prong (tripod-like) configurations, which can be modeled by…

Estimating the governing equation parameter values is essential for integrating experimental data with scientific theory to understand, validate, and predict the dynamics of complex systems. In this work, we propose a new method for…

The main aim of the paper is to introduce a new class of (semigroup-valued) measures that are ultrahomogeneous on the Boolean algebra of all clopen subsets of the Cantor space and to study their automorphism groups. A characterisation, in…

In this paper, we consider different classes of subshifts and study their perturbations obtained by forbidding sequences that contain a given word as a subword. We show that the perturbations of sofic shifts are sofic. Though not true for…

Let $K$ be a complete non-archimedean field of characteristic $0$ equipped with a discrete valuation. We establish the rationality of the Artin-Mazur zeta function on the Julia set for any subhyperbolic rational map defined over $K$ with a…

We show that the vague specification property is strictly weaker than most of the specification-like properties, by establishing its equivalence with the asymptotic average shadowing property. In particular, we see that the weak…

For Axiom A diffeomorphisms and flows, the celebrated Spectral Decomposition Theorem of Smale states that the non-wandering set decomposes into a finite disjoint union of isolated compact invariant sets, each of which is the homoclinic…

A flow on a 3-manifold is left-handed if any two ergodic invariant measures have negative linking number. We prove that on a 2-sphere of revolution whose curvature is $1/4$-pinched the geodesic flow is left-handed. Conversely, for every…

In this work, we study properties of the coordinate functions $x_\theta$ and $y_\theta$ of the dragon curve associated with the angle $\frac{\pi}{3} < \theta < \frac{5\pi}{3}$, and we prove that the box-counting dimension of its graph is…

Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…

This work investigates topological chaos for homeomorphisms of the open annulus, introducing a new set of sufficient conditions based on points with distinct rotation numbers and their topological relation to invariant continua. These…

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…

We establish that uniformly exponentially stable random dynamical systems on the half line have equivalent dynamics through a $C^m-$ conjugacy. This result was obtained for random differential equations as well as for random dynamical…

We compute the complexity of the billiard language of the regular Euclidean $N$-gons (and other families of rational lattice polygons), answering a question posed by Cassaigne-Hubert-Troubetzkoy. Our key technical result is a counting…

In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…

We prove that for any $\ell\in\NN\cup\{\infty\}$ and any $r\in \NN$, every compact smooth Riemannian manifold $\cM$ of $\dim \cM\ge 5$ carries a $C^\infty$ volume preserving nonuniformly hyperbolic diffeomorphism, which has exactly $\ell$…

In this paper we provide a sufficient condition for a Furstenberg measure generated by a finitely supported measure to be absolutely continuous. Using this, we give a very broad class of examples of absolutely continuous Furstenberg…