Two-dimensional vector fields undergoing a Hopf bifurcation are studied in a Liouville-equation approach. The Liouville equation rules the time evolution of statistical ensembles of trajectories issued from random initial conditions, but evolving under the deterministic dynamics. The time evolution of the probability densities of such statistical ensembles can be decomposed in terms of the spec...

We consider self-affine tilings in R with expansion matrix φ and address the question which matrices φ can arise this way. In one dimension, λ is an expansion factor of a self-affine tiling if and only if |λ| is a Perron number, by a result of Lind. In two dimensions, when φ is a similarity, we can speak of a complex expansion factor, and there is an analogous necessary condition, due to Thurst...

A matrix is said to have the Perron-Frobenius property (strong Perron-Frobenius property) if its spectral radius is an eigenvalue (a simple positive and strictly dominant eigenvalue) with a corresponding semipositive (positive) eigenvector. It is known that a matrix A with the Perron-Frobenius property can always be the limit of a sequence of matrices A(ε) with the strong Perron-Frobenius prope...

This special issue deals with problems related to unit roots and structural change, and the interplay between the two. The research agenda dealing with these topics have proven to be of importance for devising procedures that are reliable for inference and forecasting. Several important contributions have been made. Still, there is scope for improvements and analyses of the properties of existi...

We study and compare natural generalizations of Euclid's algorithm for polynomials with coefficients in a finite field. This leads to gcd algorithms together their associated continued fraction maps. The act on triples rely two-dimensional versions the Brun, Jacobi–Perron fully subtractive maps, respectively. first provide unified framework these then analyse various costs algorithms, including...

Let a be a mixing topological Markov shift, À a weak Perron number, q(t) a polynomial with nonnegative integer coefficients, and r a nonnegative rational. We construct a homeomorphism commuting with o whose topological entropy is \o%\q(\)q(l/\)}r. These values are shown to include the logarithms of all weak Perron numbers, and are dense in the nonnegative reals.

We study the distribution modulo m of the convergents associated with the d-dimensional Jacobi-Perron algorithm for a.e. real numbers in (0, 1) by proving the ergodicity of a skew product of the Jacobi-Perron transformation; this skew product was initially introdued in [6] for regular continued fractions.

In this paper, we present some lower bounds for the Perron root of a symmetric nonnegative matrix, which are then applied to give the lower bounds of the Perron root of a general nonnegative matrix. These bounds improve the corresponding ones in [3] and [5]. Numerical examples are supplemented to illustrate the effectiveness of the presented bounds. Mathematics subject classification (2010): 15...

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is useful to analyze fluid dynamics in geophysical contexts, as illustrated by the construction of a flow network associated to the surface circulation in the Medit...