Filters

2013 - 20152

More filters

20192
Reset filters

Settings

Type: Text × Subject: symbolic dynamics ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Statistical mechanics and information-theoretic perspectives on complexity in the Earth system
    (Basel : MDPI, 2013) Balasis, Georgios; Donner, Reik V.; Potirakis, Stelios M.; Runge, Jakob; Papadimitriou, Constantinos; Daglis, Ioannis A.; Eftaxias, Konstantinos; Kurths, Jürgen
    This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.
  • Thumbnail Image
    Item
    Chaotic orbits for systems of nonlocal equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dipierro, Serena; Patrizi, Stefania; Valdinoci, Enrico
    We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic trajectories are constructed. This is the first attempt to consider a nonlocal version of this type of dynamical systems in a variational setting and the first result regarding symbolic dynamics in a fractional framework.