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We construct the integrals of motion for the 5D deformed Kepler system with non-central potentials in $su(2)$ Yang-Coulomb monopole field. We show that these integrals form a higher rank quadratic algebra $Q(3; L^{so(4)}, T^{su(2)})\oplus…
It is well known from results of Sina\u{\i} and Bowen that a hyperbolic toral automorphism admits a Markov partition. Our aim is to generalize this concept to the nonstationary case, i.e., we associate Markov partitions to nonstationary…
The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
This work explores the intersection of time-delay embeddings, periodic orbit theory, and symbolic dynamics. Time-delay embeddings have been effectively applied to chaotic time series data, offering a principled method to reconstruct…
Rapidly increasing AI capabilities have substantial real-world consequences, ranging from AI safety concerns to labor market consequences. The Model Evaluation & Threat Research (METR) report argues that AI capabilities have exhibited…
The behavior of orbits for iterated logistic maps has been widely studied since the dawn of discrete dynamics as a research field, in particular in the context of the complex quadratic family. However, little is is known about orbit…
Given a dynamical system, we study the so-called space of shift functions thus introducing another vision on bifurcations and chaos. As an application of the obtained results, we give a partial solution to an open problem formulated in…
We initiate the study of the norm-squared of the momentum map as a rigorous tool in infinite dimensions. In particular, we calculate the Hessian at a critical point, show that it is positive semi-definite along the complexified orbit, and…
Alexandrov proved that any simplicial complex homeomorphic to a sphere with strictly non-negative Gaussian curvature at each vertex can be isometrically embedded uniquely in $\mathbb{R}^3$ as a convex polyhedron. Due to the nonconstructive…
The correlation integral and determinism are quantitative characteristics of a dynamical system based on the recurrence of orbits. For strongly non-chaotic interval maps, the determinism equals 1 for every small enough threshold. This means…
For certain types of quantum graphs we show that the random-matrix form factor can be recovered to at least third order in the scaled time $\tau$ from periodic-orbit theory. We consider the contributions from pairs of periodic orbits…
We study thermodynamic properties of an antiferromagnetic Ising model on the inverse perovskite lattice by using Monte Carlo simulations. The lattice structure is composed of corner-sharing octahedra and contains three-dimensional…
We study the asymptotic dynamics of piecewise contracting maps defined on a compact interval. For maps that are not necessarily injective, but have a finite number of local extrema and discontinuity points, we prove the existence of a…
We demonstrate some very special features of the Dirac-Born-Infeld--like (DBI) gravitational counter-term in AdS$_4$ spacetime, in the context of holography with a sharp radial cut-off. We show that the three-sphere partition function is…
Some frustrated magnets and superconducting arrays possess unusual symmetries that cause the free energy or other physics of a $D$-dimensional quantum or classical problem to be that of a different problem in a reduced dimension $d<D$.…
We study complex one-dimensional parameter slices in a three-parameter family of rational maps with two free critical points, obtained by imposing the existence of periodic orbits with prescribed multipliers. Using explicit…
In this article we continue the study of the collapse of three inelastic particles in dimension $d \geq 2$, complementing the results we obtained in its companion paper. We focus on the particular case of the nearly-linear inelastic…
Everything you ever wanted to know about what has come to be known as ``chaotic mixing:'' This paper describes the evolution of localised ensembles of initial conditions in 2- and 3-D time-independent potentials which admit both regular and…