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The notion of time is derived as a parameter of statistical ensemble representing the underlying system. Varying population numbers of microstates in statistical ensemble result in different expectation values corresponding to different…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
We present new applications of parity inversion and time-reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal…
The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over $2\%$, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
A physical pendulum with variable point of suspension (and, as an outcome, variable inertia moment) is experimentally analysed. In particular, the period of the small oscillations as a function of position of the suspension point is…
We study the problem of reconstructing and predicting the future of a dynamical system by the use of time-delay measurements of typical observables. Considering the case of too few measurements, we prove that for Lipschitz systems on…
A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative…
Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can behave unexpectedly when the signal between the vertices are time delayed. It has been shown for a very…
Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement…
Finite-time coherent sets represent minimally mixing objects in general nonlinear dynamics, and are spatially mobile features that are the most predictable in the medium term. When the dynamical system is subjected to small parameter…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
We describe an experiment dedicated to the study of the trajectories of a ball bouncing randomly on a vibrating plate. The system was originally used, considering a sinusoidal vibration, to illustrate period doubling and the route to chaos.…
We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the…
In the study of some dynamical systems the limsup set of a sequence of measurable sets is often of interest. The shrinking targets and recurrence are two of the most commonly studied problems that concern limsup sets. However, the zero-one…
We investigate the short-time dynamics of a delta-function potential barrier on an initially confined wave-packet. There are mainly two conclusions: A) At short times the probability density of the first particles that passed through the…
A general scheme for construction of dynamical systems able to learn generation of the desired kinds of dynamics through adjustment of their internal structure is proposed. The scheme involves intrinsic time-delayed feedback to steer the…