Hardware security for an Internet of Things or cyber physical system drives the need ubiquitous cryptography to different sensing infrastructures in these fields. In particular, generating strong cryptographic keys on such resource-constrained device depends a lightweight and cryptographically secure random number generator. this research work, we have introduced new hardware chaos-based pseudorandom generator, which is mainly based deletion Hamilton cycle within N-cube (or vectorial...

Abstract It is well known that a family of tent-like maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value turning point. In this note we prove following result: if consider cusp at point, recover response. More precisely, let T ɛ be such generated by point 0 perturbation and h corresponding invariant density. We <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo...

In a uniformly hyperbolic system, we consider the problem of finding optimal infinitesimal perturbation to apply from certain set $P$ feasible ones, maximally increase expectation given observation function. We perturb system both by composing with diffeomorphism near identity or adding deterministic dynamics. cases, using fast adjoint response formula, show that linear operator, which associates on dynamics, is bounded in terms $C^{1,\alpha}$ norm perturbation. Under assumption strictly...

We prove that if a non-autonomous system has in certain sense fast convergence to equilibrium (faster than any power law behavior), then the time τr(x,y) needed for typical point x enter first ball B(y,r) centered at y, with small radius r, scales as local dimension of measure μ i.e., limr→0log⁡τr(x,y)−log⁡r=dμ(y). apply general result concrete systems different kinds, showing such logarithm asymptotically autonomous solenoidal maps and mean field coupled expanding maps.

Abstract We consider the problem of optimal linear response for deterministic expanding maps circle. To each infinitesimal perturbation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> </mml:mrow> </mml:math> a circle map T we (i) expectation an observation function and (ii) isolated spectral points transfer operator . In case, under mild conditions on set feasible perturbations show there is...

We consider a random dynamical system on $\mathbb{R}^d$, whose dynamics is defined by stochastic differential equation. The annealed transfer operator associated with such systems kernel operator. Given set of feasible infinitesimal perturbations $P$ to this kernel, support in certain compact set, and specified observable function $\phi: \mathbb{R}^d \to \mathbb{R}$, we study which perturbation produces the greatest change expectation $\phi$. establish conditions under optimal uniquely...

Abstract In this paper we prove that the Poincaré map associated to a Lorenz-like flow has exponential decay of correlations with respect Lipschitz observables. This implies hitting time satisfies logarithm law. The τ r ( x , 0 ) is needed for orbit point enter ball B centered at small radius first time. As decreases its asymptotic behavior power law whose exponent related local dimension physical measure : each such d μ exists, holds almost . similar way, it possible consider quantitative...

We consider the question of computing invariant measures from an abstractpoint view. Here, a measure means finding algorithm which canoutput descriptions up to any precision. work in general framework (computable metric spaces) where this problem can be posed precisely. will find as fixed points transfer operator. In case, result ensures computability isolated computable map. give conditions under operator is on suitable set. This implies many 'regular enough' and among them physical...

We describe a framework in which it is possible to develop and implement algorithms for the approximation of invariant measures dynamical systems with given bound on error approximation. Our approach based general statement fixed points operators between normed vector spaces, allowing an explicit estimation error. show flexibility our by applying piecewise expanding maps indifferent points. how required estimations can be implemented compute densities up $L^{1}$ or $L^\infty $ distance. also...

We prove the existence of noise induced order in Matsumoto–Tsuda model, where it was originally discovered 1983 by numerical simulations. This is a model famous Belousov–Zhabotinsky reaction, chaotic chemical and consists one dimensional random dynamical system with additive noise. The simulations showed that an increase amplitude causes Lyapunov exponent to decrease from positive negative; we give mathematical proof this transition. method use relies on some computer aided estimates...

We prove that if a system has superpolynomial (faster than any power law) decay of correlations then the time τ r (x, x 0 ) needed for typical point to enter first ball B(x , r) centered in with small radius scales as local dimension at i.e.This result is obtained by proving kind dynamical Borel-Cantelli lemma wich holds also systems having polinomial correlations.

We present a general setting in which the formula describing linear response of physical measure perturbed system can be obtained. In this we obtain an algorithm to rigorously compute response. apply our results expanding circle maps. particular, examples where compute, up pre-specified error -norm, maps under stochastic and deterministic perturbations. Moreover, example L1-norm, intermittent family at boundary; i.e. when unperturbed is doubling map.

We consider transformations preserving a contracting foliation, such that the associated quotient map satisfies Lasota-Yorke inequality. prove transfer operator, acting on suitable normed spaces, has spectral gap (on which we have quantitative estimation). As an application Lorenz-like two dimensional maps (piecewise hyperbolic with unbounded contraction and expansion rate): those systems show estimate for their statistical stability. Under deterministic perturbations of system size...

This paper introduces a method for detecting joint angles by using piezoresistive strain sensitive materials, as carbon loaded rubbers are. Materials used can be screen-printed onto fabrics to provide garments with sensing apparatus able reconstruct human postures and gestures. The main differences between this approach the previous ones, core of work, is rigorous proof that small local curvatures layers constituting electrogoniometers, resistance depends only on total curvature not...

We consider toral extensions of hyperbolic dynamical systems. prove that its quantitative recurrence (also with respect to given observables) and hitting time scale behavior depend on the arithmetical properties extension. By this we show those systems have a polynomial decay correlations $C^{r}$ observables, give estimations for exponent, which $r$ system. also examples kind having not shrinking target property, trivial limit distribution return statistics.

We consider a general relation between fixed point stability of suitably perturbed transfer operators and convergence to equilibrium (a notion which is strictly related decay correlations). apply this deterministic perturbations class (piecewise) partially hyperbolic skew products whose behavior on the preserved fibration dominated by expansion base map. In particular, we results power law mixing toral extensions. It turns out that in case, dependence physical measure small perturbations,...

We show a linear response statement for fixed points of family Markov operators, which are perturbations mixing and regularizing operators. apply the to random dynamical systems on interval given by deterministic map T with additive noise (distributed according bounded variation kernel). prove these systems, also providing explicit formulas both changes in kernel. The holds mild assumptions system, allowing have critical points, contracting expanding regions. our theory topological maps...

Quantitative recurrence indicators are defined by measuring the first entrance time of orbit a point x in decreasing sequence neighborhoods another y.It is proved that these a.e.greater or equal to local dimension at y.Moreover, estimation sharph if some mild assumptions on statistic return times satisfied.These can hence be used have an efficient numerical invariant measure.

We show an elementary method to obtain (finite time and asymptotic) computer assisted explicit upper bounds on convergence equilibrium (decay of correlations) escape rates for systems satisfying a Lasota Yorke inequality. The are deduced from the ones suitable approximations system's transfer operator. also present some rigorous experiments nontrivial example.

We consider a class of maps from the unit square to itself preserving contracting foliation and inducing one-dimensional map having an absolutely continuous invariant measure. show how physical measure those systems can be rigorously approximated with explicitly given bound on error respect Wasserstein distance. present rigorous implementation our algorithm using interval arithmetics, result computation non-trivial example Lorenz-like two-dimensional its attractor, obtaining statement local...