258 research outputs found
Fractal diffusion coefficient from dynamical zeta functions
No full textDynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi–Ruelle generalization of the Milnor–Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero
Periodic orbit theory of strongly anomalous transport
No full textWe establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical appearance of phase transitions in the spectrum of transport exponents is explained
Universality of algebraic decays in Hamiltonian systems
No full textHamiltonian systems with a mixed phase space typically exhibit an algebraic decay of correlations and of Poincare' recurrences, with numerical experiments over finite times showing system-dependent power-law exponents. We conjecture the existence of a universal asymptotic decay based on results for a Markov tree model with random scaling factors for the transition probabilities. Numerical simulations for different Hamiltonian systems support this conjecture and permit the determination of the universal exponent
Anomalous deterministic transport
No full textWe present a series of results on deterministic transport in chaotic system, obtained in the framework of periodic orbits theory. The emphasis is on intermittent systems, where deviations from complete chaos may induce anomalies on the asymptotic moments’ growth
Deterministic (Anomalous) Transport
No full textWe introduce and review deterministic (anomalous) transport along the lines of the thermodynamic formalism. For simple models such deterministic techniques yield exact formulas of transport coefficients in terms of periodic orbits, which can be evaluated via cycle expansions
Recycling Parrondo games
No full textWe consider a deterministic realization of Parrondo games and use periodic orbit theory to analyze their asymptotic behavior
On the origin of long-range correlations in texts
No full textThe complexity of human interactions with social and natural
phenomena is mirrored in the way we describe our experiences
through natural language. In order to retain and convey such a
high dimensional information, the statistical properties of our linguistic
output has to be highly correlated in time. An example are
the robust observations, still largely not understood, of correlations
on arbitrary long scales in literary texts. In this paper we
explain how long-range correlations flow from highly structured
linguistic levels down to the building blocks of a text (words, letters,
etc..). By combining calculations and data analysis we show
that correlations take form of a bursty sequence of events once
we approach the semantically relevant topics of the text. The
mechanisms we identify are fairly general and can be equally
applied to other hierarchical settings
Anomalous Transport of Light in Complex Systems
No full textWe intend to start a detailed study of the transport properties of light in inhomogeneous strongly disordered systems. Indeed, due to the fact that there is a huge variety of precision techniques to measure its properties, to the fact that is possible to study both coherent and incoherent properties and to the fact that photons can be considered has non-interacting in practically all the interesting cases, light can be regarded as a useful paradigm for the study of transport processes. Experimental results in this framework will be a stimulus for the study of analytical method which will eventually provide new results suited to be checked in the laboratory. The project will thus profit from the combined approach: the optical-experimental and the mathematical physics one
Internal-wave billiards in trapezoids and similar tables
No full textWe call internal-wave billiard the dynamical system of a point particle that
moves freely inside a planar domain (the table) and is reflected by its
boundary according to this rule: reflections are standard Fresnel reflections
but with the pretense that the boundary at any collision point is either
horizontal or vertical (relative to a predetermined direction representing
gravity). These systems are point particle approximations for the motion of
internal gravity waves in closed containers, hence the name. For a class of
tables similar to rectangular trapezoids, but with the slanted leg replaced by
a general curve with downward concavity, we prove that the dynamics has only
three asymptotic regimes: (1) there exist a global attractor and a global
repellor, which are periodic and might coincide; (2) there exists a beam of
periodic trajectories, whose boundary (if any) comprises an attractor and a
repellor for all the other trajectories; (3) all trajectories are dense (that
is, the system is minimal). Furthermore, in the prominent case where the table
is an actual trapezoid, we study the sets in parameter space relative to the
three regimes. We prove in particular that the set for (1) has positive measure
(giving a rigorous proof of the existence of Arnol'd tongues for internal-wave
billiards), whereas the sets for (2) and (3) are non-empty but have measure
zero.Comment: Final preprint for Nonlinearity, 29 pages, 11 figure
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