Integrability and non-integrability of periodic non-autonomous Lyness recurrences

This paper studies non-autonomous Lyness type recurrences of the form x_{n+2}=(a_n+x_n)/x_{n+1}, where a_n is a k-periodic sequence of positive numbers with prime period k. We show that for the cases k in {1,2,3,6} the behavior of the sequence x_n is simple(integrable) while for the remaining cases satisfying k not a multiple of 5 this behavior can be much more complicated(chaotic). The cases k multiple of 5 are studied separately.

Integrability and non-integrability of periodic non-autonomous Lyness recurrences (revised and enlarged version)

This paper studies non-autonomous Lyness type recurrences of the form xn+2 = (an+xn+1)=xn, where fang is a k-periodic sequence of positive numbers with primitive period k. We show that for the cases k 2 f1; 2; 3; 6g the behavior of the sequence fxng is simple (integrable) while for the remaining cases satisfying this behavior can be much more complicated (chaotic). We also show that the cases where k is a multiple of 5 present some di erent features.

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attractors are observed. Even in the quasiperiodic regime, attractors with a certain degree of strangeness may exist. From the observed multifractal dimensions, the deterministic nature of the chaotic oscillations is clearly identified.

Emprego de sílica gel organicamente modificada e impressa ionicamente para pré-concentração seletiva on-line de íons cobre

The present work purposes the preparation of a silica gel sorbent organically modified with 2-aminoethyl-3-aminobutylmethyldimethoxysilane (AAMDMS) and imprinted with Cu2+ ions by means surface imprinting technique and its use for selective on-line sorbent preconcentration of Cu2+ ions with further UV-VIS spectrophotometric determination by flow injection analysis. The Cu2+-imprinted silica gel, when compared with non imprinted silica gel and silica gel, showed from the binary mixture of Cu2+/Ni2+ relative selectivity coefficient (k') of 6.84 and 5.43 and 6.64 and 19.83 for the mixture Cu2+/Pb2+, thus demonstrating higher selectivity of Cu2+-imprinted silica gel towards Cu2+ ions. Under optimized condition, the on-line preconcentration method provided detection limit of 3.4 μg L-1 and linear range ranging from 30.0 up to 300.0 μg L-1 (r = 0.995). The accuracy of method was successfully assessed by analyzing different kind of spiked water samples with recovery values ranging from 92.2 up to 103.0%.