Due to fluctuations around the metric entropy of chaotic dynamical systems there exists a spectrum of invariant dynamical scaling indices, complementary to the range of invariant static scaling indices which have been discovered and apphed recently. The basic scaling behavior in both cases is shown to be rooted in the thermodynamic formalism of dynamical systems. An explicit simple example of t...

Topological Chern indices are related to the number of rotational states in each molecular vibrational band. Modification of the indices is associated to the appearance of "band degeneracies," and exchange of rotational states between two consecutive bands. The topological dynamical origin of these indices is demonstrated through a semiclassical approach, and their values are computed in two ex...

The use of performance indices to measure the quality response of dynamical systems is studied in this paper. A definition of a general performance index is proposed which is easy to compute, easy to interpret, and flexible enough to account for different cases commonly presented in practice. The index is tested over several dynamical responses obtained from different systems obtaining good res...

Let U ⊂ R2 be an open subset and f : U → R2 be an arbitrary local homeomorphism with Fix f {p}. We compute the fixed point indices of the iterates of f at p, iR2 f, p , and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincaré index formula without differentiability assumptions. Our techniques apply equally to both orientation preserving and orientation reversing...

We prove several results majorizing the sequences of Kronecker and/or Jordan indices obtainable after small perturbations to a given matrix pencil. The proofs are simple consequences of a theory of majorization for semi-innnite integer sequences, developed in this paper. In particular , new simple bounds are proved on the indices obtainable after appending a single row or column to a matrix pen...

The information contained in any given experimental time series can be utilized more exhaustively when transition probabilities between states are studied rather than state probabilities alone. Using advanced techniques of time series analysis, it is shown that deviations from dynamical randomness indicate evidence for unexpected temporal correlation features in selected data sets taken from a ...