Related papers: Ergodic theory and visualization. II. Harmonic mes…
M. Kruskal showed that each continuous-time nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. When the nearly-periodic system is also Hamiltonian, Noether's theorem implies the existence…
This paper presents an active search trajectory synthesis technique for autonomous mobile robots with nonlinear measurements and dynamics. The presented approach uses the ergodicity of a planned trajectory with respect to an expected…
In search and surveillance applications in robotics, it is intuitive to spatially distribute robot trajectories with respect to the probability of locating targets in the domain. Ergodic coverage is one such approach to trajectory planning…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a version of Hofbauer's Markov diagram, (ii) the…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…
We are interested in a non-local partial differential equation modeling equal mitosis. We prove that the solutions present persistent asymptoticoscillations and that the convergence to this periodic behavior, in suitable spaces of weighted…
We analytically study the time evolution of the expectation values of observables in periodically kicked many-body quantum systems. Starting from an initial state, we compute both the transient and the long-time properties of the…
Ergodic optimization is the study of problems relating to maximizing orbits, maximizing invariant measures and maximum ergodic averages. An orbit of a dynamical system is called f-maximizing if the time average of the real-valued function f…
We show that elements of control theory, together with an application of Harris' ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
Quantum phases of matter have many relevant applications in quantum computation and quantum information processing. Current experimental feasibilities in diverse platforms allow us to couple two or more subsystems in different phases. In…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
The correlation between level velocities and eigenfunction intensities provides a new way of exploring phase space localization in quantized non-integrable systems. It can also serve as a measure of deviations from ergodicity due to quantum…
A method is proposed for constraining the Galactic gravitational potential from high precision observations of the phase space coordinates of a system of relaxed tracers. The method relies on an "ergodic" assumption that the observations…
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…
We apply a method inspired by Ratner's work on quantitative mixing for the geodesic flow (Ergod. Theory Dyn. Syst., 1987) and developed by Burger (Duke Math. J., 1990) to study ergodic integrals for horocycle flows. We derive an explicit…
The analysis of chaotic signals with time-frequency methods is considered. For this purpose, two new transformations are presented which consist in the decomposition of a signal onto an orthogonal set of respectively linear and hyperbolic…