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## Fibonacci bimodal maps

VARGAS, Edson
Fonte: AMER INST MATHEMATICAL SCIENCES Publicador: AMER INST MATHEMATICAL SCIENCES
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
66.57%
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.; CNPq-Brasil[304517/2005-4]; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

## Symbolic Dynamics and chaotic synchronization

Gracio, Clara; Caneco, Acilina; Rocha, José
Fonte: World Scientific Publicador: World Scientific
Tipo: Parte de Livro
ENG
Relevância na Pesquisa
26.25%
Chaotic communications schemes based on synchronization aim to provide security over the conventional communication schemes. Symbolic dynamics based on synchronization methods has provided high quality synchronization [5]. Symbolic dynamics is a rigorous way to investigate chaotic behavior with finite precision and can be used combined with information theory [13]. In previous works we have studied the kneading theory analysis of the Duffing equation [3] and the symbolic dynamics and chaotic synchronization in coupled Duffing oscillators [2] and [4]. In this work we consider the complete synchronization of two identical coupled unimodal and bimodal maps. We relate the synchronization with the symbolic dynamics, namely, defining a distance between the kneading sequences generated by the map iterates in its critical points and defining n-symbolic synchronization. We establish the synchronization in terms of the topological entropy of two unidirectional or bidirectional coupled piecewise linear unimodal and bimodal maps. We also give numerical simulations with coupled Duffing oscillators that exhibit numerical evidence of the n-symbolic synchronization.

## Second eigenvalue of transition matrix associated to iterated maps

Fernandes, Sara; Sousa Ramos, José
Tipo: Artigo de Revista Científica
POR
Relevância na Pesquisa
46.33%
Abstract: We study the properties of the second eigenvalue of the transition matrix in unimodal and bimodal map’s families. We use in particular the relation with the mixing rate and apply this to classify families of isentropic bimodal maps. We present also a study which show the convergence of this quantity in those families.

## CONDUCTANCE AND MIXING TIME IN DISCRETE DYNAMICAL SYSTEMS

Fernandes, Sara; Jayachandran, Sumitha
Fonte: WORLD SCIENTIFIC Publicador: WORLD SCIENTIFIC
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
25.91%
We have introduced the notion of conductance in discrete dynamical systems using the known results from graph theory applied to systems arising from the iteration of continuous functions. The conductance allowed differentiating several systems with the same topological entropy, characterizing them from the point of view of the ability of the system to go out from a small subset of the state space. There are several other definitions of conductance and the results differ from one to another. Our goal is to understand the meaning of each one concerning the dynamical behaviour in connection with the decay of correlations and mixing time. Our results are supported by computational techniques using symbolic dynamics, and the tree-structure of the unimodal and bimodal maps.

## Kneading theory analysis of the Duffing equation

Gracio, Clara; Caneco, Acilina; Rocha, José
Fonte: Chaos, Solitons & Fractals Publicador: Chaos, Solitons & Fractals
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
26.12%
The purpose of this paper is to study the symmetry effect on the kneading theory for symmetric unimodal maps and for symmetric bimodal maps. We obtain some properties about the kneading determinant for these maps, that implies some simplifications in the usual formula to compute, explicitly, the topological entropy. As an application, we study the chaotic behaviour of the two-well Duffing equation with forcing.

## Kneading theory analysis of the Duffing equation

Caneco, Acilina; Rocha, Jose; Gracio, Clara
Fonte: Chaos, Solitons & Fractals Publicador: Chaos, Solitons & Fractals
Tipo: Artigo de Revista Científica
POR
Relevância na Pesquisa
26.12%
The purpose of this paper is to study the symmetry effect on the kneading theory for symmetric unimodal maps and for symmetric bimodal maps. We obtain some properties about the kneading determinant for these maps, that implies some simplifications in the usual formula to compute, explicitly, the topological entropy. As an application, we study the chaotic behaviour of the two-well Duffing equation with forcing.

## Synchronization and basins of Synchronized States in Two-Dimensional piecewise Maps via Coupling Three Pieces of One-Dimensional Maps

Fournier-Prunaret, Daniele; Rocha, José; Caneco, Acilina; Fernandes, Sara; Grácio, Clara
Fonte: World Scientific Publicador: World Scientific
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.12%
This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

## Invariants for the topological characterization of the iteration of diﬀerentiable functions – the bimodal case

Correia, M. C.; Ramos, C. C.; Vinagre, Sandra
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
26.36%
We consider dynamical systems deﬁned by a particular class of diﬀerentiable functions, as ﬁxed state space. The dynamics is given by the iteration of an operator induced by a polynomial map which belongs to an appropriate family of isentropic bimodal interval maps. We characterize topologically these dynamical systems, in particular using the invariants deﬁned for the iteration of the bimodal interval maps.

## Invariants for the topological characterization of the iteration of differentiable functions – the bimodal case

Correia, Maria F.; Ramos, Carlos; Vinagre, Sandra
Tipo: Artigo de Revista Científica
POR
Relevância na Pesquisa
26.36%
We consider dynamical systems defined by a particular class of differentiable functions, as fixed state space. The dynamics is given by the iteration of an operator induced by a polynomial map which belongs to an appropriate family of isentropic bimodal interval maps. We characterize topologically these dynamical systems, in particular using the invariants defined for the iteration of the bimodal interval maps.

## Late-orogenic, mantle-derived, bimodal magmatism in the southern Adelaide Foldbelt, South Australia / by Simon P. Turner.

Turner, Simon P.
Tipo: Tese de Doutorado Formato: 250859 bytes; application/pdf
Relevância na Pesquisa
25.91%
Late-orogenic magmas are common to many foldbelts, suggesting a causal link between this thermal pulse and the cessation of deformation. An investigation of such a late-orgenic magnetic suite is made in the southern Adelaide Foldbelt. The suite is biomodal with mafic dykes and plutons accompanied by high-silica granites and rhyolites. It is argued that these mafic and felsic intrusives are both thermally and compositionally related.; Thesis (Ph.D.)--University of Adelaide, Dept. of Geology and Geophysics, 1992; Copies of author's previously published articles inserted.; Bibliography : leaves 179-196.; v, 196, [43] leaves : ill. (some col.), maps ; 30 cm.; Title page, contents and abstract only. The complete thesis in print form is available from the University Library.

## A Genealogy for Finite Kneading Sequences of Bimodal Maps on the Interval

Ringland, John; Tresser, Charles
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.11%
We generate all the finite kneading sequences of one of the two kinds of bimodal map on the interval, building each sequence uniquely from a pair of shorter ones. There is a single pair at generation 0, with members of length 1. Concomitant with this genealogy of kneading sequences is a unified genealogy of all the periodic orbits. (6/93); Comment: Text, in PostScript form, is compressed and uuencoded. Figures are in Uuencoded tar-compressed bundle which expands to a directory containing 10 Postscript files one for each of the 10 figures. Total size when expanded is approximately 0.5Mb. If preferred, hard copy is available by request from the authors

## Bifurcations of homoclinic orbits in bimodal maps

Hansen, Kai T.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.25%
We discuss the bifurcation structure of homoclinic orbits in bimodal one dimensional maps. The universal structure of these bifurcations with singular bifurcation points and the web of bifurcation lines through the parameter space are described. The bifurcations depend on two parameters (codimension 2 bifurcations). We find the bifurcation lines exactly in a symbolic dynamics parameter plane and numerically in the parameter planes of a polynomial map and a piecewise linear map.; Comment: 11 pages, uuencoded compressed PostScript

## The Computational Complexity of Symbolic Dynamics at the Onset of Chaos

Lakdawala, Porus
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.11%
In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis for modelling this region is the Universal Turing Machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.; Comment: 1 reference corrected, 1 reference added, minor changes in body of manuscript

## Merging history of three bimodal clusters

Maurogordato, S.; Sauvageot, J. -L.; Bourdin, H.; Cappi, A.; Benoist, C.; Ferrari, C.; Mars, G.; Houairi, K.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.11%
We present a combined X-ray and optical analysis of three bimodal galaxy clusters selected as merging candidates at z ~ 0.1. These targets are part of MUSIC (MUlti--Wavelength Sample of Interacting Clusters), which is a general project designed to study the physics of merging clusters by means of multi-wavelength observations. Observations include spectro-imaging with XMM-Newton EPIC camera, multi-object spectroscopy (260 new redshifts), and wide-field imaging at the ESO 3.6m and 2.2m telescopes. We build a global picture of these clusters using X-ray luminosity and temperature maps together with galaxy density and velocity distributions. Idealized numerical simulations were used to constrain the merging scenario for each system. We show that A2933 is very likely an equal-mass advanced pre-merger ~ 200 Myr before the core collapse, while A2440 and A2384 are post-merger systems ~ 450 Myr and ~1.5 Gyr after core collapse, respectively). In the case of A2384, we detect a spectacular filament of galaxies and gas spreading over more than 1 h^{-1} Mpc, which we infer to have been stripped during the previous collision. The analysis of the MUSIC sample allows us to outline some general properties of merging clusters: a strong luminosity segregation of galaxies in recent post-mergers; the existence of preferential axes --corresponding to the merging directions-- along which the BCGs and structures on various scales are aligned; the concomitance...

## Omega from the COBE-DMR anisotropy maps

Cayon, L.; Martinez-Gonzalez, E.; Sanz, J. L.; Sugiyama, N.; Torres, S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.05%
We have made a likelihood statistical analysis of the angular correlations in the {\it COBE}-DMR two-year sky maps by Monte Carlo simulation of the temperature fluctuations. We assume an open universe and consider as primordial power spectrum the Harrison-Zeldovich one, $P(k)=Ak$. We find that the flatness of the universe is not implied by the data. The quadrupole normalization amplitude, $Q_{rms-PS}$, is related to the density parameter, $\Omega$, by $Q_{rms-PS} = 10.67 + 55.81 \Omega - 128.59 \Omega^2 + 81.26 \Omega^3\ \mu$K. We have determined the p.d.f. of $\Omega$ due to cosmic plus sampling (i.e. $20^\circ$ galactic cut) variance which generically shows a bimodal shape. The uncertainty as given by the r.m.s. is $\approx 0.35$, therefore to better constrain $\Omega$ experiments sensitive to higher multipoles ($l>20$) should be considered.; Comment: 4 pages, 2 figures, 1 table, uuencoded encapsulated postscript file. Figure 2 available upon request

## Irreducible complexity of iterated symmetric bimodal maps

Lampreia, J. P.; Severino, R.; Ramos, J. Sousa
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.43%
We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a $\ast$-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the *-product induced on the associated Markov shifts.

## Simulated X-ray Cluster Temperature Maps

Onuora, Lesley I.; Kay, Scott T.; Thomas, Peter A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
26.12%
Temperature maps are presented of the 9 largest clusters in the mock catalogues of Muanwong et al. for both the Preheating and Radiative models. The maps show that clusters are not smooth, featureless systems, but contain a variety of substructure which should be observable. The surface brightness contours are generally elliptical and features that are seen include cold clumps, hot spiral features, and cold fronts. Profiles of emission-weighted temperature, surface brightness and emission-weighted pressure across the surface brightness discontinuities seen in one of the bimodal clusters are consistent with the cold front in Abell 2142 observed by Markevitch et al.; Comment: Submitted to Monthly Notices Royal Astronomical Society

## Submillimetre maps of the edge-on galaxy NGC 891

Israel, F. P.; van der Werf, P. P.; Tilanus, R. P. J.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
25.91%
Broadband continuum images of the edge-on galaxy NGC 891 at 850 and 450 microns are presented. These images are qualitatively very similar to the 1300 micron and CO images obtained by others. With respect to the 850 micron continuum, CO is strongest in the socalled `molecular ring', and weakest at the largest radii sampled. Inside the molecular ring, the CO/850 micron ratio is somewhat less than in the ring, but higher than in the remainder of the disk. The integrated far-infrared emission from NGC 891 is dominated by small particles shortwards of 100 microns. Longwards of 100 micron, the emission can be equally well fitted by a single population of large dust grains at 21 K, or a bimodal population of grains at temperatures of 18 K and 27 K. The circumnuclear disk is at a temperature of at least 50 K, and probably much higher.; Comment: 4 pages, 2 Figures, LaTeX, Accepted for A&A Letters

## The Link between Magnetic Fields and Filamentary Clouds: Bimodal Cloud Orientations in the Gould Belt

Li, Hua-bai; Fang, Min; Henning, Thomas; Kainulainen, Jouni
Tipo: Artigo de Revista Científica