1,721,046 research outputs found
Fillotassi: il più nell'uno
No full textI tentativi di modellizzazione matematica della fillotassi hanno una storia lunga e interessante. L'analisi dettagliata di uno di essi, il modello cilindrico di van Iterson, fornisce uno spunto esemplare per alcune valutazioni di natura epistemologica sulla modellizzazione scientifica in biologia. In particolare mette il luce il fatto che una forma debba essere riguardata innanzitutto come il risultato della dinamica di crescita della pianta, dunque della sua storia singolare
Zeta-function and distribution of periodic orbits of toral automorphisms
No full textIn this paper we study the distribution properties of periodic orbits for the linear hyperbolic automorphisms of the d-torus. We first obtain an explicit expression of the dynamical zeta function and prove general equidistribution results similar to those obtained for axiom A flows. We then study in detail some families of periodic orbits living on invariant prime lattices: they have the property that the integral of any character along any single orbit can be reduced to a number theoretic exponential sum over a finite field. This fact enables us to obtain explicit estimates on their asymptotic distributional properties
On the spectrum of Farey and Gauss maps
No full textIn this paper we introduce Hilbert spaces of holomorphic functions given by generalized Borel and Laplace transforms which are left invariant by the transfer operators of the Farey map and its induced transformation, the Gauss map, respectively. By means of a suitable operator-valued power series we are able to study simultaneously the spectrum of both these operators along with the analytic properties of associated dynamical zeta functions. This construction establishes an explicit connection between previously unrelated results of Mayer and Rugh (see [Ma1] and [Rug])
On systems with finite ergodic degree
No full textWe study the ergodic theory of a class of symbolic dynamical systems with finite ergodic degree, both in the infinite and finite measure case
‘Mathematics’ and ‘physics’ in the science of harmonics
Full text linkSome aspects of the role that the science of harmonics has played in the history of science are discussed in the light of Russo’s investigation about the history of the concepts of ‘mathematics’ and ‘physics’
Renewal sequences and intermittency
No full textIn this paper we examine the generating function Φ(z) of a renewal sequence arising from the distribution of return times in the ‘turbulent’ region for a class of piecewise affine interval maps introduced by Gaspard and Wang(1) and studied by several authors(2−8). We prove that it admits a meromorphic continuation to the entire complex z-plane with a branch cut along the ray (1, +∞). Moreover we compute the asymptotic behaviour of the coefficients of its Taylor expansion at z = 0. From this, the exact polynomial asympotics for the rate of mixing when the invariant measure is finite and of the scaling rate when it is infinite are obtained
Understanding complex behaviour. Some remarks on method and intepretation, in `Chaos and Complexity', (Torino, October 5-11, 1987), R. Livi, S. Ruffo, S. Ciliberto and M. Buiatti eds., World Scientific.
No full textWe discuss some recent issues concerning the methodology to extract information from a chaotic dynamical system and its interpretation
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