相关论文: Rigorous computation of escape times for parameter…
We develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of one-dimensional maps $f_a (x) = a - x^2$. We illustrate the…
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…
We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter values in the quadratic family. We compute a possibly small…
We study the rate of growth of ratios of intervals delimited by the post-critical orbit of a map in the quasi-quadratic family $x\mapsto -|x|^\alpha +a.$ The critical order $\alpha$ is an arbitrary real number $\alpha>1.$ The range of the…
The escape mechanism of the four hill potential is explored. A thorough numerical investigation takes place in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space in…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
This paper presents a new algorithm based on interval methods for rigorously constructing inner estimates of feasible parameter regions together with enclosures of the solution set for parameter-dependent systems of nonlinear equations in…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
We study the Escape Problem for discrete-time linear dynamical systems over compact semialgebraic sets. We establish a uniform upper bound on the number of iterations it takes for every orbit of a rational matrix to escape a compact…
The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of…
We investigate the evolution of families of periodic orbits in a bisymmetrical potential made up of a two-dimensional harmonic oscillator with only one quartic perturbing term, in a number of resonant cases. Our main objective is to compute…
We calculate rigorous bounds on the Hausdorff dimension of the attractor at the accumulation of the period-doubling cascade for families of maps with quadratic, cubic, and quartic critical point. To do this, we express the attractors as the…
We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and…
This paper investigates the critical-time criteria as a security metric for controlled systems subject to sharp input anomalies (attack, fault), characterized by having high impact in a reduced amount of time (e.g. denial-of-service, attack…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
The correct computation of orbits of discrete dynamical systems on the interval is considered. Therefore, an arbitrary-precision floating-point approach based on automatic error analysis is chosen and a general algorithm is presented. The…
Considering the problem of risk-sensitive parameter estimation, we propose a fairly wide family of lower bounds on the exponential moments of the quadratic error, both in the Bayesian and the non--Bayesian regime. This family of bounds,…
This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time $t_{\text{mix}}$ of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from…
We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical…
The multiplier $\lambda_n$ of a periodic orbit of period $n$ can be viewed as a (multiple-valued) algebraic function on the space of all complex quadratic polynomials $p_c(z)=z^2+c$. We provide a numerical algorithm for computing critical…