Related papers: Two-dimensional time-reversible ergodic maps with …

The time reversibility characteristic of Hamiltonian mechanics has long been extended to nonHamiltonian dynamical systems modeling nonequilibrium steady states with feedback-based thermostats and ergostats. Typical solutions are…

Simple time-reversible systems can generate {\it irreversible} flows satisfying the Second Law of Thermodynamics. Maps, and equivalent random walks, can also do this. We study a pair of time-reversible Baker Maps, $N2$ and $N3$, which…

The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…

Fundamental interactions are either fully or nearly symmetric under time reversal. But macroscopic phenomena have a definite arrow of time. Though there is no convergence on the origin of time's preferential direction, many researchers…

Time reversal symmetric triangular maps of the unit square are introduced with the property that the time evolution of one of their two variables is determined by a piecewise expanding map of the unit interval. We study their statistical…

This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt's and Zerm\'elo's paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the {\it irreversible}…

Deterministic and time-reversible nonequilibrium molecular dynamics simulations typically generate "fractal" [ fractional-dimensional ] phase-space distributions. Because these distributions and their time-reversed twins have zero phase…

Let $f:\mathbb{CP}^2\dashrightarrow\mathbb{CP^2}$ be a rational map with algebraic and topological degrees both equal to $d\geq 2$. Little is known in general about the ergodic properties of such maps. We show here, however, that for an…

We give piecewise affine maps on the unit cube whose symbolic representation is the Dyck shift. This leads to a different way of verifying the chaotic nature of this system, including the computation of entropy.

We study some new dynamical systems where the corresponding piecewise linear flow is neither time reversible nor measure preserving. We create a dissipative system by starting with a finite polysquare translation surface, and then modifying…

This paper studies a parametrized family of familiar generalized baker maps, viewed as simple models of time-reversible evolution. Mapping the unit square onto itself, the maps are partly contracting and partly expanding, but they preserve…

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the…

We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…

This study examines the tree models of mildly dissipative diffeomorphisms on the disk $\D$. These models are one-dimensional dynamical systems with ergodic aperiodic data as well as some properties of the original dynamics. The focus of…

We present extensive numerical investigations on the ergodic properties of two identical Pomeau-Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but…

Time reversal of vast classes of phenomena has direct implications with predictability, causality and the second principle of thermodynamics. We analyze in detail time reversibility of a paradigmatic dissipative nonlinear dynamical system,…

We investigate a decomposition of a unital Lindblad dynamical map of an open quantum system into two distinct types of mapping on the Hilbert-Schmidt space of quantum states. One component of the decomposed map corresponds to reversible…

Ergodic exploration has spawned a lot of interest in mobile robotics due to its ability to design time trajectories that match desired spatial coverage statistics. However, current ergodic approaches are for continuous spaces, which require…