Related papers: Unpredictable sequences and Poincar\'e chaos
Reasoning about unpredicted change consists in explaining observations by events; we propose here an approach for explaining time-stamped observations by surprises, which are simple events consisting in the change of the truth value of a…
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of such randomness involve precise uncertainty models, and it…
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…
In this paper, a new concept, i.e. ultra-chaos, is proposed for the first time. Unlike a normal-chaos, statistical properties such as the probability density functions (PDF) of an ultra-chaos are sensitive to tiny disturbances. We…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
This paper addresses the classical problem of determining the set of possible states of a linear discrete-time system subject to bounded disturbances from measurements corrupted by bounded noise. These so-called uncertainty sets evolve with…
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\delta}-chaotic if and…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…
Non-deterministic chaos is a form of low-dimensional dynamics which is characterized by the existence of a countable set of {\em sensitive decision points} (SDP's). Away from these points, the dynamics is well-behaved. Near these points,…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…