Design and implementation of recursive DNS server

Bonanno, T.; Kim, HyoungJun; Park, Jungsoo

doi:10.1109/icact.2006.206050

Cited by 1 publication

(1 citation statement)

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“…A slightly weaker result was recently proved in (Bonanno, 2006) and argues that for almost all α and β one can find two positive constants C i , i = 1, 2 such that C 1 t 3 ≤…”

Section: Topological Complexity Of the Triangle Mapmentioning

confidence: 92%

On ergodic and mixing properties of the triangle map

Horvat

Esposti

Isola

et al. 2009

Physica D: Nonlinear Phenomena

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In this paper we study in detail, both analytically and numerically, the dynamical properties of the triangle map, a piecewise parabolic automorphism of the two-dimensional torus, for different values of the two independent parameters defining the map. The dynamics is studied numerically by means of two different symbolic encoding schemes, both relying on the fact that it maps polygons to polygons: in the first scheme we consider dynamically generated partitions made out of suitable sets of disjoint polygons, in the second we consider the standard binary partition of the torus induced by the discontinuity set. These encoding schemes are studied in detail and shown to be compatible, although not equivalent. The ergodic properties of the triangle map are then investigated in terms of the Markov transition matrices associated to the above schemes and furthermore compared to the spectral properties of the Koopman operator in L2(T2). Finally, a stochastic version of the triangle map is introduced and studied. A simple heuristic analysis of the latter yields the correct statistical and scaling behaviours of the correlation functions of the original map.Comment: 45 pages, 30 figure

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“…A slightly weaker result was recently proved in (Bonanno, 2006) and argues that for almost all α and β one can find two positive constants C i , i = 1, 2 such that C 1 t 3 ≤…”

Section: Topological Complexity Of the Triangle Mapmentioning

confidence: 92%