Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Área residencial estratégica Sector l’Estació (Barberà del Vallès)

El ARE ‘Sector Estació’, es una propuesta para generar una centralidad en un entorno de baja densidad, utilizando como foco un gran vacío-parque que viene generado por la afección aérea del Aeródromo de Sabadell, y que resuelva la conexión viaria interna a través del ferrocarril. Se trata de generar un tejido residencial diverso y versátil, rico en gradaciones entre espacio público y privado, que incorpore criterios sencillos de urbanismo sostenible, y conseguir un espacio de identidad y de referencia en el municipio.

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.

On periodic solutions of 2-periodic Lyness difference equations

We study the existence of periodic solutions of the non--autonomous periodic Lyness' recurrence u_{n+2}=(a_n+u_{n+1})/u_n, where {a_n} is a cycle with positive values a,b and with positive initial conditions. It is known that for a=b=1 all the sequences generated by this recurrence are 5-periodic. We prove that for each pair (a,b) different from (1,1) there are infinitely many initial conditions giving rise to periodic sequences, and that the family of recurrences have almost all the even periods. If a is not equal to b, then any odd period, except 1, appears.

Articles indexats publicats per investigadors del Campus de Terrassa: 2011

Aquest informe recull els 209 treballs publicats per 198 investigadors/es del Campus de Terrassa en revistes indexades al Journal Citation Report durant el 2011

Pièges de souvenirs

Postprint (published version)

La Biblioteca del Campus del Baix Llobregat: memòria 2006

Postprint (published version)

Autors més prolífics Campus del Baix Llobregat (CBL) - 2011

S'inclouen el 30% de les publicacions científiques (articles i participacions a congressos) publicades l'any 2011 per autors de: CTTC, EETAC, ESAB, ICFO, i Ide

Congressos amb més articles Campus del Baix Llobregat (CBL) - 2011

Es presenta la llista de congressos en les que més han participat els autors del CBL ordenat per centres. Si el centre no apareix vol dir que els congressos en el que han participat els seus autors no están buidats a l’SCOPUS.

Producció científica del Campus del Baix Llobregat. Desembre 2012

Preprint

Producció Científica del Campus del Baix Llobregat (CBL): gener-maig 2012

Preprint

Producció Científica del Campus del Baix Llobregat (CBL): Juny-agost 2012

Preprint

Producció científica del Campus del Baix Llobregat. Novembre 2012

Preprint

Producció científica del Campus del Baix Llobregat. Octubre 2012

Preprint