One-dimensional projective subdynamics of uniformly mixing shifts of finite type

2014 ◽  
Vol 35 (6) ◽  
pp. 1962-1999
Author(s):  
MICHAEL H. SCHRAUDNER
Keyword(s):  
Finite Type ◽  
Sufficient Condition ◽  
Mixing Conditions ◽  
One Dimensional ◽  
Strongly Irreducible ◽  
Topologically Mixing ◽  
Stark Contrast ◽  
The One

We investigate under which circumstances the projective subdynamics of multidimensional shifts of finite type can be non-sofic. In particular, we give a sufficient condition ensuring the one-dimensional projective subdynamics of such $\mathbb{Z}^{d}$ systems to be sofic and we show that this condition is already met (along certain, respectively all, sublattices) by most of the commonly used uniform mixing conditions. (Examples of the different situations are given.) Complementary to this we are able to prove a characterization of one-dimensional projective subdynamics for strongly irreducible $\mathbb{Z}^{d}$ shifts of finite type for every $d\geq 2$: in this setting the class of possible subdynamics coincides exactly with the class of mixing $\mathbb{Z}$ sofics. This stands in stark contrast to the much more diverse situation in merely topologically mixing multidimensional shifts of finite type.

scholarly journals Topologically completely positive entropy and zero-dimensional topologically completely positive entropy

2017 ◽  
Vol 38 (5) ◽  
pp. 1894-1922
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Finite Type ◽  
Sufficient Condition ◽  
Positive Entropy ◽  
Two Dimensional ◽  
Completely Positive ◽  
Shift Of Finite Type ◽  
One Dimensional ◽  
Zero Entropy ◽  
The Difference

In a previous paper [Pavlov, A characterization of topologically completely positive entropy for shifts of finite type. Ergod. Th. & Dynam. Sys.34 (2014), 2054–2065], the author gave a characterization for when a $\mathbb{Z}^{d}$-shift of finite type has no non-trivial subshift factors with zero entropy, a property which we here call zero-dimensional topologically completely positive entropy. In this work, we study the difference between this notion and the more classical topologically completely positive entropy of Blanchard. We show that there are one-dimensional subshifts and two-dimensional shifts of finite type which have zero-dimensional topologically completely positive entropy but not topologically completely positive entropy. In addition, we show that strengthening the hypotheses of the main result of Pavlov [A characterization of topologically completely positive entropy for shifts of finite type. Ergod. Th. & Dynam. Sys.34 (2014), 2054–2065] yields a sufficient condition for a $\mathbb{Z}^{d}$-shift of finite type to have topologically completely positive entropy.

A Note on Hidden Transient Chaos in the Lorenz System

2017 ◽  
Vol 18 (5) ◽  
pp. 427-434 ◽  
Author(s):  
Quan Yuan ◽  
Fang-Yan Yang ◽  
Lei Wang
Keyword(s):  
Rayleigh Number ◽  
Lorenz System ◽  
Critical Value ◽  
Transient Chaos ◽  
Topological Horseshoe ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
The One

AbstractIn this paper, the classic Lorenz system is revisited. Some dynamical behaviors are shown with the Rayleigh number $\rho $ somewhat smaller than the critical value 24.06 by studying the basins characterization of attraction of attractors and tracing the one-dimensional unstable manifold of the origin, indicating some interesting clues for detecting the existence of hidden transient chaos. In addition, horseshoes chaos is verified in the famous system for some parameters corresponding to the hidden transient chaos by the topological horseshoe theory.

scholarly journals Lipoarabinomannans: characterization of the multiacylated forms of the phosphatidyl-myo-inositol anchor by NMR spectroscopy

1999 ◽  
Vol 337 (3) ◽  
pp. 453-460 ◽  
Author(s):  
Jérôme NIGOU ◽  
Martine GILLERON ◽  
Germain PUZO
Keyword(s):  
Molecular Basis ◽  
Quantum Correlation ◽  
Analytical Approach ◽  
31P Nmr ◽  
Multiple Quantum ◽  
Double Negative ◽  
Bacillus Calmette Guerin ◽  
One Dimensional ◽  
The One

Lipoarabinomannans, which exhibit a large spectrum of immunological activities, emerge as the major antigens of mycobacterial envelopes. The lipoarabinomannan structure is based on a phosphatidyl-myo-inositol anchor whose integrity has been shown to be crucial for lipoarabinomannan biological activity and particularly for presentation to CD4/CD8 double-negative αβT cells by CD1 molecules. In this report, an analytical approach was developed for high-resolution 31P-NMR analysis of native, i.e. multiacylated, lipoarabinomannans. The one-dimensional 31P spectrum of cellular lipoarabinomannans, from Mycobacterium bovis Bacillus Calmette–Guérin, exhibited four 31P resonances typifying four types of lipoarabinomannans. Two-dimensional 1H-31P heteronuclear multiple-quantum-correlation/homonuclear Hartmann–Hahn analysis of the native molecules showed that these four types of lipoarabinomannan differed in the number and localization of fatty acids (from 1 to 4) esterifying the anchor. Besides the three acylation sites previously described, i.e. positions 1 and 2 of glycerol and 6 of the mannosyl unit linked to the C-2 of myo-inositol, we demonstrate the existence of a fourth acylation position at the C-3 of myo-inositol. We report here the first structural study of native multiacylated lipoarabinomannans, establishing the structure of the intact phosphatidyl-myo-inositol anchor. Our findings would help gain more understanding of the molecular basis of lipoarabinomannan discrimination in the binding process to CD1 molecules.

scholarly journals Solutions of the nonlinear paraxial equation due to laser plasma–interactions

2004 ◽  
Vol 22 (1) ◽  
pp. 69-74 ◽  
Author(s):  
F. OSMAN ◽  
R. BEECH ◽  
H. HORA
Keyword(s):  
Laser Plasma ◽  
Theoretical Study ◽  
Semiclassical Limit ◽  
General Setting ◽  
One Dimension ◽  
One Dimensional ◽  
Laser Plasma Interactions ◽  
Weak Limits ◽  
The One

This article presents a numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit ħ → 0 of the nonlinear paraxial equation. In a general setting of both dimension and nonlinearity, the essential differences between the “defocusing” and “focusing” cases are observed. Numerical comparisons of the oscillations are made between the linear (“free”) and the cubic (defocusing and focusing) cases in one dimension. The integrability of the one-dimensional cubic nonlinear paraxial equation is exploited to give a complete global characterization of the weak limits of the oscillations in the defocusing case.

scholarly journals Subharmonic orbits in an anharmonic oscillator

1997 ◽  
Vol 38 (3) ◽  
pp. 307-315 ◽  
Author(s):  
J. R. Christie ◽  
K. Gopalsamy ◽  
M. P. Panizza
Keyword(s):  
Differential Equations ◽  
Autonomous System ◽  
Anharmonic Oscillator ◽  
Dynamical Behaviour ◽  
Sufficient Condition ◽  
One Dimensional ◽  
Perturbed System ◽  
Melnikov Theory ◽  
The One ◽  
Subharmonic Orbits

AbstractIn a recent paper, Christie and Gopalsamy [2] used Melnikov's method to establish a sufficient condition for the existence of chaotic behaviour, in the sense of Smale, in a particular time-periodically perturbed planar autonomous system of ordinary differential equations. They then concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. In this paper, the same system is considered and a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensional anharmonic oscillator system.

scholarly journals Homology for one-dimensional solenoids

2017 ◽  
Vol 121 (2) ◽  
pp. 219 ◽  
Author(s):  
Massoud Amini ◽  
Ian F. Putnam ◽  
Sarah Saeidi Gholikandi
Keyword(s):  
Finite Type ◽  
Homology Theory ◽  
One Dimensional ◽  
Axiom A ◽  
Group Invariant ◽  
Dimension Group ◽  
Basic Set ◽  
The One ◽  
Topological Dynamical Systems ◽  
Smale Spaces

Smale spaces are a particular class of hyperbolic topological dynamical systems, defined by David Ruelle. The definition was introduced to give an axiomatic description of the dynamical properties of Smale's Axiom A systems when restricted to a basic set. They include Anosov diffeomeorphisms, shifts of finite type and various solenoids constructed by R. F. Williams. The second author constructed a homology theory for Smale spaces which is based on (and extends) Krieger's dimension group invariant for shifts of finite type. In this paper, we compute this homology for the one-dimensional generalized solenoids of R. F. Williams.

scholarly journals Observation of broad-band water waveguiding in shallow water: a revival

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Fabián Sepúlveda-Soto ◽  
Diego Guzmán-Silva ◽  
Edgardo Rosas ◽  
Rodrigo A. Vicencio ◽  
Claudio Falcón
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Open Channel ◽  
Fluid Layer ◽  
Broad Band ◽  
Shallow Water Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Phenomena

Abstract We report on the observation and characterization of broad-band waveguiding of surface gravity waves in an open channel, in the shallow water limit. The waveguide is constructed by changing locally the depth of the fluid layer, which creates conditions for surface waves to propagate along the generated guide. We present experimental and numerical results of this shallow water waveguiding, which can be straightforwardly matched to the one-dimensional water wave equation of shallow water waves. Our work revitalizes water waveguiding research as a relevant and controllable experimental setup to study complex phenomena using waveguide geometries.

On the stability of some solutions of the Stefan problem

1991 ◽  
Vol 2 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Riccardo Ricci ◽  
Xie Weiqing
Keyword(s):  
Stefan Problem ◽  
Travelling Wave ◽  
Sufficient Condition ◽  
Travelling Wave Solutions ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Necessary And Sufficient ◽  
Travelling Wave Front

We investigate the stability of travelling wave solutions of the one-dimensional under-cooled Stefan problem. We find a necessary and sufficient condition on the initial datum under which the free boundary is asymptotic to a travelling wave front. The method applies also to other types of solutions.

Sign in / Sign up

Export Citation Format

Share Document