Dynamical Systems Papers of the Week

However, existing reviews usually organise the literature by algorithm category or application scenario, making it difficult to explain both the behavior ultimately produced by the system and the logic through which the controller achieves its objectives. This scoping review aims to map the distribution and thematic structure of the literature on reinforcement learning-based control of nonlinear dynamical systems, from 2021 to 2026.

For each $n$, choose $\omega_1,\ldots,\omega_n$ independently according to these probabilities and set $F=f_{\omega_n}\circ\cdots\circ f_{\omega_1}$. We prove that there exists $\alpha>0$ such that, with probability at least $1-e^{-\alpha n}$, the correlations of any two Hölder observables $\phi,\psi$ under $F^m$ are bounded by $e^{-\alpha n}\|\phi\|_{C^\beta}\|\psi\|_{C^\beta}$, for all $m\leq e^{\alpha n}$.

We investigate connections between operator spectra, complex dynamics, and determinants for wreath product groups.

Here we propose riddled basin geometry as a unifying dynamical systems mechanism: every initialization leading to one solution lies arbitrarily close to initializations leading to different solutions, forming a fat fractal with structure at arbitrarily fine scales.

In this paper, we study Egorov's theorem for Laplacian eigenfunctions on compact hyperbolic surfaces in Zelditch's quantization.

We consider the competitive dynamics of two viral strains using compartmental epidemiological models that incorporate temporary cross-immunity with a discrete time delay, and are calibrated using wastewater surveillance data.

This study presents a comprehensive dynamical analysis of a ratio-dependent reaction–diffusion prey–predator model, with an emphasis on nonlinear oscillatory behavior and the evolution of spatiotemporal patterns.

Here, we used a multivariate dynamical systems approach to analyze simultaneously recorded neural activity, autonomic physiology, and behavior during rest and during attentive and distracted listening to spoken narratives.

Near the neutral fixed point of an intermittent map, a single entrance into a small target can be followed by a long run of consecutive visits, so the number of visits need not follow its mean. We study targets $[0,u_n]$ for iid random compositions of Liverani-Saussol-Vaienti maps with a bounded parameter law that is regularly varying at its minimum $\alpha\in(0,1)$; this includes a single map.

We develop a divergence-kernel method for jointly optimizing neural SDE drift and diffusion fields and the initial Gaussian distribution, using losses that depend directly on the terminal density.

We prove that, for commuting unitary representations $U,V$ of a countable amenable group $G$, the averages $$ D_F=\frac1{|F|}\sum_{g\in F}U_g^*V_g $$ have a common selfadjoint weak operator limit along all left and right \Folner{} sequences, with strong* convergence along two-sided sequences.

We consider mixing for a scalar advected by random vector fields, such as solutions to stochastic fluid equations.

For each integer $p\geq2$, we consider the upper capacity entropy scale obtained by dividing the $p$-fold logarithm of an orbit covering number by the $(p-1)$-fold logarithm of time.

We study the equality case of the inequalities between the Lyapunov spectrum and the Harder--Narasimhan slopes of a semi-simple local system with non-expanding cusp monodromy over a finite-area hyperbolic surface.

We study mixed random-quasiperiodic cocycles whose one-step laws evolve along an ergodic environment.

We conduct extensive two-parameter analyses of both the full and phase-reduced models, revealing rich multi-rhythmic dynamics and transitions among coexisting rhythmic states.

We introduce natural expansiveness, a notion of expansiveness for non-invertible dynamical systems which is defined by using the natural extension.