Related papers: Two-dimensional time-reversible ergodic maps with …
We introduce two abstract constructions for building new measurable dynamical systems from existing ones and study their ergodic properties. The first of these constructions, a "reciprocal transformation," produces a type of non-singular…
The Kaplan-Yorke conjecture states that for "typical" dynamical systems with a physical measure, the information dimension and the Lyapunov dimension coincide. We explore this conjecture in a neighborhood of a system for which the two…
We introduce two parametrized families of piecewise affine maps on $[0,1]^2$ and $[0,1]^3$, as generalizations of the heterochaos baker maps which were introduced and investigated in [Y. Saiki, H. Takahasi, J. A. Yorke, Nonlinearity, 34…
A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted…
A discrete dynamical system known as Arnold's Discrete Cat Map (Arnold's DCM) is given by (x_t+1, y_t+1) = (x_t + y_t, x_t + 2y_t) mod N; which acts on a two-dimensional square coordinate grid of size Nx?N. The defining characteristic of…
We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
The semi-invertible version of Oseledets' multiplicative ergodic theorem providing a decomposition of the underlying state space of a random linear dynamical system into fast and slow spaces is deduced for a strongly measurable cocycle on a…
Driven-dissipative systems define a broad class of non-equilibrium systems where an external drive (e.g. laser) competes with a dissipative environment. The steady state of dynamics is generically distinct from a thermal state…
As a model to provide a hands-on, elementary understanding of "vortex dynamics", we introduce a piecewise linear non-invertible map called a twisted baker map. We show that the set of hyperbolic repelling periodic points with complex…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…
Random operators constitute fundamental building blocks of models of complex systems yet are far from fully understood. Here, we explain an asymmetry emerging upon repeating identical isotropic (uniformly random) operations. Specifically,…
We construct examples of volume-preserving uniquely ergodic (and hence minimal) real-analytic diffeomorphisms on odd-dimemsional spheres
We study geometry of two-dimensional models of conformal space-time based on the group of Moebius transformation. The natural geometric invariants, called cycles, are used to linearise Moebius action. Conformal completion of the space-time…
We discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…
Conditions are obtained for a Gaussian vector autoregressive time series of order $k$, VAR($k$), to have univariate margins that are autoregressive of order $k$ or lower-dimensional margins that are also VAR($k$). This can lead to…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
We introduce a framework for the reconstruction and representation of functions in a setting where these objects cannot be directly observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The…
We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of…
In reversible dynamical systems, it is frequently of importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend…