Related papers: Two-dimensional time-reversible ergodic maps with …
Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum…
We study the dynamics of inertial particles in two dimensional incompressible flows. The Maxey-Riley equation describing the motion of inertial particles is used to construct a four dimensional dissipative bailout embedding map. This map…
We examine the conjecture of equivalence of nonequilibrium ensembles for turbulent flows in two-dimensions (2D) in a dual-cascade setup. We construct a formally time-reversible Navier-Stokes equations in 2D by imposing global constraints of…
Continuous image morphing is a classical task in image processing. The metamorphosis model proposed by Trouv\'e, Younes and coworkers casts this problem in the frame of Riemannian geometry and geodesic paths between images. The associated…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows…
In this paper, we study a discrete system of entities residing on a two-dimensional square grid. Each entity is modelled as a node occupying a distinct cell of the grid. The set of all $n$ nodes forms initially a connected shape $A$.…
Treating the two-dimensional Minkowski space as a Wick rotated version of the complex plane, we characterize the causal automorphisms in two-dimensional Minkowski space as the M\"{a}rzke-Wheeler maps of a certain class of observers. We also…
How does the arrow of time (dissipative, irreversible behavior) emerge from time-reversible Hamiltonian mechanics? Two ingredients are needed: the underlying system must be ergodic or phase-mixing, and our knowledge of the system must be…
The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic…
We define a class of dynamical systems on the sphere analogous to the baker map on the torus. The classical maps are characterized by dynamical entropy equal to ln 2. We construct and investigate a family of the corresponding quantum maps.…
We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet…
The Ray--Knight theorems show that the local time processes of various path fragments derived from a one-dimensional Brownian motion $B$ are squared Bessel processes of dimensions $0$, $2$, and $4$. It is also known that for various…
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional surfaces. We consider one and two parameter general unfoldings…
Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…
We consider the trajectories of points on $\mathbb{S}^{d - 1}$ under sequences of certain folding maps associated with reflections. The main result characterizes collections of folding maps that produce dense trajectories. The minimal…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…
We revisit a two-temperature Nos\'e-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in…