scholarly journals Two problems on weighted shifts in linear dynamics

2021 ◽  
pp. 1
Author(s):  
Frédéric Bayart
Keyword(s):  
Weighted Shifts ◽  
Linear Dynamics

Topologically transitive skew-products of operators

2009 ◽  
Vol 30 (1) ◽  
pp. 33-49 ◽  
Author(s):  
FRÉDÉRIC BAYART ◽  
GEORGE COSTAKIS ◽  
DEMETRIS HADJILOUCAS
Keyword(s):  
Linear Operators ◽  
Skew Product ◽  
Weighted Shifts ◽  
Linear Dynamics ◽  
Topologically Transitive ◽  
Skew Products ◽  
Product Systems ◽  
Hypercyclic Vectors ◽  
Backward Shift

AbstractThe purpose of the present paper is to provide a link between skew-product systems and linear dynamics. In particular, we give a criterion for skew-products of linear operators to be topologically transitive. This is then applied to certain families of linear operators including scalar multiples of the backward shift, backward unilateral weighted shifts, composition, translation and differentiation operators. We also prove the existence of common hypercyclic vectors for certain families of skew-product systems.

scholarly journals Chaos and frequent hypercyclicity for composition operators

2021 ◽  
pp. 1-19
Author(s):  
Udayan B. Darji ◽  
Benito Pires
Keyword(s):  
Recent Result ◽  
Large Class ◽  
Composition Operators ◽  
Intimate Relationship ◽  
Invertible Operator ◽  
Weighted Shift ◽  
Weighted Shifts ◽  
Linear Dynamics ◽  
Chaotic Operator

Abstract The notions of chaos and frequent hypercyclicity enjoy an intimate relationship in linear dynamics. Indeed, after a series of partial results, it was shown by Bayart and Ruzsa in 2015 that for backward weighted shifts on $\ell _p(\mathbb {Z})$ , the notions of chaos and frequent hypercyclicity coincide. It is with some effort that one shows that these two notions are distinct. Bayart and Grivaux in 2007 constructed a non-chaotic frequently hypercyclic weighted shift on $c_0$ . It was only in 2017 that Menet settled negatively whether every chaotic operator is frequently hypercylic. In this article, we show that for a large class of composition operators on $L^{p}$ -spaces, the notions of chaos and frequent hypercyclicity coincide. Moreover, in this particular class, an invertible operator is frequently hypercyclic if and only if its inverse is frequently hypercyclic. This is in contrast to a very recent result of Menet where an invertible operator frequently hypercyclic on $\ell _1$ whose inverse is not frequently hypercyclic is constructed.

Neural identification of systems with linear dynamics and static nonlinear elements

1999 ◽  
Author(s):  
R. C. L. Oliveira ◽  
F. M. Azevedo ◽  
J. M. Barreto ◽  
C. T. da Costa
Keyword(s):  
Linear Dynamics

An Exercise in a Transdisciplinary Approach for New Knowledge Paradigms

2014 ◽  
Vol 3 (3) ◽  
pp. 114-143
Author(s):  
Gabriel Crumpei ◽  
Maricel Agop ◽  
Alina Gavriluţ ◽  
Irina Crumpei
Keyword(s):  
Quantum Mechanics ◽  
20Th Century ◽  
Chaos Theory ◽  
Fractal Geometry ◽  
Science And Religion ◽  
Transdisciplinary Approach ◽  
Linear Dynamics ◽  
New Knowledge ◽  
Religious Perspectives ◽  
Energy Information

Abstract In this paper, we aim at an exercise that is transdisciplinary, involving science and religion, and interdisciplinary, involving disciplines and theories which appeared in the second half of the 20th century (e.g., topology, chaos theory, fractal geometry, non-linear dynamics, all of which can be found in the theory of complex systems). The latter required the reformulation of quantum mechanics theories starting with the beginning of the century, based on the substance-energy-information triangle. We focus on information and we also attempt a transdisciplinary approach to the imaginary from a psychological - physical - mathematical perspective, but the religious perspectives find their place along with the philosophical or even philological vision

Low pressure hydrocephalus and ventriculomegaly: hysteresis, non-linear dynamics, and the benefits of CSF diversion

2002 ◽  
Vol 16 (6) ◽  
pp. 555-561 ◽  
Author(s):  
M. S. Lesniak ◽  
R. E. Clatterbuck ◽  
D. Rigamonti ◽  
M. A. Williams
Keyword(s):  
Low Pressure ◽  
Linear Dynamics ◽  
Non Linear ◽  
Csf Diversion

Unification of Gauge Forces and Gravity using Tangled Vortex Knots and Entanglement Dynamics

2020 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Field Theory ◽  
Short Range ◽  
Gauge Fields ◽  
Entanglement Dynamics ◽  
Unified Field Theory ◽  
Linear Dynamics ◽  
Unified Field ◽  
The Standard Model ◽  
Theory Of Everything ◽  
The Continuum

In this paper, the statistics of excitation-tangles in a postulated background ideal-superfluid field is studied. The structure of the Standard Model is derived in terms of tangle vortex-knots and soliton. Gravity is observed in terms of torsion and curvature in the continuum. In this way, non-linear dynamics and excitations give rise to a unified field theory as well as a Theory of Everything. As a result of this unification, spacetime and matter are shown to be fundamentally equivalent, while gauge fields arise from reorientation and excitations of the the fundamental underlying field. Finally, the equivalence of topological and quantum entanglement is explored to posit a theory of everything in terms of long- and short-range entanglement between fundamental quantum units (bits) of information.

Non-linear dynamics in DIS at NLO

2017 ◽  
Author(s):  
Giovanni Antonio Chirilli
Keyword(s):  
Linear Dynamics ◽  
Non Linear
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