Related papers: Discrete Dynamical Systems Embedded in Cantor Sets
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical…
We derive sufficient conditions for a dynamical systems to have a set of irregular points with full topological entropy. Such conditions are verified for some nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms…
The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological…
The purpose of this paper is to present an example of a C1 (in the Fr\'echet sense) discrete dynamical system in a infinite-dimensional separable Hilbert space for which the origin is an exponentially asymptotically stable fixed point, but…
Reliable data-driven estimation of Shannon entropy from small data sets, where the number of examples is potentially smaller than the number of possible outcomes, is a critical matter in several applications. In this paper, we introduce a…
We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
Neural networks often learn task-specific latent representations that fail to generalize to novel settings or tasks. Conversely, humans learn discrete representations (i.e., concepts or words) at a variety of abstraction levels (e.g.,…
The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…
Dynamical phase transitions (DPT) are characterized by nonanalytical time evolution of the dynamical free energy. For general 2-band systems in one and two dimensions (eg. SSH model, Kitaev-chain, Haldane model, p+ip superconductor, etc.),…
The time evolution of complex systems usually can be described through stochastic processes. These processes are measured at finite resolution, what necessarily reduces them to finite sequences of real numbers. In order to relate these data…
In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a…
For the generic continuous map and for the generic homeomorphism of the Cantor space, we study the dynamics of the induced map on the space of probability measures, with emphasis on the notions of Li-Yorke chaos, topological entropy,…