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The aim of this Workshop is to promote interdisciplinary discussion among researchers working in areas related to dynamics, chaos and their applications. New results will be presented. It is our intention that the talks be accessible to a wide audience. We are inviting and expect a diverse audience with ample time for scientific exchanges.
We develop a method to detect the presence of integrals of the motion in symplectic rational maps, by representing these maps over finite fields and examining their orbit structure. We find markedly different orbit statistics depending upon whether the map is integrable or not.
We study a 4-fold symmetric kicked-oscillator map with sawtooth kick function. For the values of the kick amplitude λ = 2 cos(2πp/q) with rational p/q, the dynamics is known to be pseudochaotic, with no stochastic web of non-zero Lebesgue measure. We show that this system can be represented as a piecewise affine map of the unit square —the so-called local… (More)
We investigate the reduction to finite fields of polynomial automorphisms of the plane, which lead to invertible dynamics (permutations) of a finite space. We provide evidence that, if the map of the plane is non-integrable, then the presence or absence of a type of time-reversal symmetry called R-reversibility produces a clear signature in the cycle… (More)
We study propagation of pulses along one-way coupled map lattices, which originate from the transition between two superstable states of the local map. The velocity of the pulses exhibits a staircase-like behaviour as the coupling parameter is varied. For a piece-wise linear local map, we prove that the velocity of the wave has a Devil's staircase… (More)
We reduce planar measure-preserving rational maps over finite fields, and study their discrete dynamics. We show that application to the orbit analysis over these fields of the Hasse-Weil bound for the number of points on an algebraic curve gives a strong indication of the existence of an integral for the map. Moreover, the method is ideally suited to… (More)
Multistable coupled map lattices typically support traveling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile allows a reduction of the infinitely dimensional dynamics to a one-dimensional circle homeomorphism, whose rotation number gives the propagation velocity. The mode locking… (More)
an introductory course franco vivaldi school of mathematical sciences Preface This is the textbook for the course Mathematical Writing, offered to second year undergraduate students in mathematics at Queen Mary, University of London. Instructions on writing mathematics are normally given to postgraduate students , to prepare them to write research articles… (More)