Fibonacci bimodal maps

We introduce the Fibonacci bimodal maps on the interval and show that their two turning points are both in the same minimal invariant Cantor set. Two of these maps with the same orientation have the same kneading sequences and, among bimodal maps without central returns, they exhibit turning points with the strongest recurrence as possible.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.

EIGENVALUES of FIBONACCI STOCHASTIC ADDING MACHINE

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Band edge states of the < n >=0 gap of Fibonacci photonic lattices

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Eits: Combinatorics, Potential and Genre

Eits is a work of fiction, a non-traditional novel whose structure is largely determined by an Oulipian-style constraint. The constraint in Eits is culled from the album names and song titles of the band Explosions in the Sky. Each album corresponds to a chapter in the novel, and the language of each album title must be used in some way as an introduction to each chapter. Within each chapter (album), song titles correspond to numbered sections where each title must appear as is in the first sentence of that section. This not only dictates, to some degree, the direction of the text that will follow, but, looking ahead, the title of the next section will dictate where this section must arrive. From this, a narrative naturally takes shape. Albums/chapters appear chronologically, according to each album's release date, and within each album/chapter, songs/sections appear in the order they do on the album. This is, perhaps, the most straightforward way of ordering the received language of the constraint, the possibilities beyond this exponential. Eits is a novel that shifts in form, providing a texture to the space and reading experience of the novel, all in hopes of creating a space in which content and form inform and push each other to new limits. Eits is never satisfied to settle on one form for too long, and it is in the movement between forms that the narrative develops in interesting ways. Eits demonstrates the combinatoric possibilities inherent in language, and this exploration of potential highlights the reciprocal relationship between writing and reading. As Eits builds upon a limited language set, it explores and exploits the combinatory possibilities that language allows for both writer and reader. It demonstrates that all combinatoric potentialities, visible or not, always co-exist in the same time and space, and in this infinite space, individuals are invited to be writers and readers in simultaneity.

Deficient generalized Fibonacci maximum path graphs /

"UILU-ENG 78 1739."