Strong nonuniform spectrum for arbitrary growth rates

2017 ◽  
Vol 19 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Luis Barreira ◽  
Davor Dragičević ◽  
Claudia Valls
Keyword(s):  
Growth Rates ◽  
Exponential Dichotomy ◽  
Complete Characterization ◽  
Initial Time ◽  
Exponential Dependence ◽  
Conditional Stability ◽  
Exponential Dichotomies ◽  
Exponential Rates ◽  
Nonuniform Exponential Dichotomies

We consider the notion of strong nonuniform spectrum for a nonautonomous dynamics with discrete time obtained from a sequence of matrices, which is defined in terms of the existence of strong nonuniform exponential dichotomies with an arbitrarily small nonuniform part. The latter exponential dichotomies are ubiquitous in the context of ergodic theory and correspond to have both lower and upper bounds along the stable and unstable directions, besides possibly a nonuniform conditional stability although with an arbitrarily small exponential dependence on the initial time. Moreover, we consider arbitrary growth rates instead of only the usual exponential rates. We give a complete characterization of the possible strong nonuniform spectra and for a Lyapunov regular trajectory, we show that the spectrum is the set of Lyapunov exponents. In addition, we provide explicit examples of nonautonomous dynamics for all possible strong nonuniform spectra. A remarkable consequence of our results is that for a sequence of matrices [Formula: see text], either [Formula: see text] does not admit a strong exponential dichotomy for any [Formula: see text], or if [Formula: see text] admits an exponential dichotomy for some [Formula: see text], then it also admits a strong exponential dichotomy for that [Formula: see text]. We emphasize that this result is not in the literature even in the special case of uniform exponential dichotomies.

Lyapunov theorems for exponential dichotomies in Hilbert spaces

2016 ◽  
Vol 27 (04) ◽  
pp. 1650033 ◽  
Author(s):  
Davor Dragičević ◽  
Ciprian Preda
Keyword(s):  
Hilbert Spaces ◽  
Exponential Dichotomy ◽  
Complete Characterization ◽  
Linear Operators ◽  
Nonlinear Perturbations ◽  
Exponential Behavior ◽  
Exponential Dichotomies ◽  
Linear And Nonlinear ◽  
Unstable Direction

For a nonautonomous dynamics defined by a sequence of linear operators, we obtain a complete characterization of the notion of a uniform exponential dichotomy in terms of the existence of appropriate Lyapunov sequences. In sharp contrast to previous results, we consider the case of noninvertible dynamics, thus requiring only the invertibility of operators along the unstable direction. Furthermore, we deal with operators acting on an arbitrary Hilbert space. As a nontrivial application of our work, we study the persistence of uniform exponential behavior under small linear and nonlinear perturbations.

NONUNIFORM EXPONENTIAL BEHAVIOUR AND TOPOLOGICAL EQUIVALENCE

2015 ◽  
Vol 58 (2) ◽  
pp. 279-291
Author(s):  
LUIS BARREIRA ◽  
LIVIU HORIA POPESCU ◽  
CLAUDIA VALLS
Keyword(s):  
Asymptotic Behaviour ◽  
Ergodic Theory ◽  
Canonical Form ◽  
Exponential Dichotomy ◽  
Topological Equivalence ◽  
Exponential Dichotomies ◽  
Exponential Behaviour ◽  
Nonuniform Exponential Dichotomies ◽  
Nonuniform Exponential Dichotomy ◽  
Topological Conjugacies

AbstractWe show that any evolution family with a strong nonuniform exponential dichotomy can always be transformed by a topological equivalence to a canonical form that contracts and/or expands the same in all directions. We emphasize that strong nonuniform exponential dichotomies are ubiquitous in the context of ergodic theory. The main novelty of our work is that we are able to control the asymptotic behaviour of the topological conjugacies at the origin and at infinity.

COMPLETE CHARACTERIZATION OF BREAKUP OF 9Be BY α-α COINCIDENCE MEASUREMENTS

2011 ◽  
Vol 20 (04) ◽  
pp. 835-838 ◽  
Author(s):  
R. RAFIEI ◽  
D. H. LUONG ◽  
D. J. HINDE ◽  
M. DASGUPTA ◽  
R. DU RIETZ
Keyword(s):  
Relative Energy ◽  
Complete Characterization ◽  
Exponential Dependence ◽  
Q Value ◽  
Weakly Bound ◽  
Surface Separation ◽  
Coincidence Measurements ◽  
Α Particles ◽  
Probability Of Capture

The breakup mechanisms for 9 Be have been studied through coincident detection of the breakup α particles at sub-barrier energies, where the probability of capture of a charged breakup fragment by the target nucleus is negligible. Combining the reconstructed reaction Q-value and the relative energy of the two coincident breakup α particles a complete picture of breakup dynamics has been obtained. The measurements reveal breakup processes which are fast enough (~ 10-22 s) to affect fusion, called prompt breakup. It is shown that prompt breakup is triggered predominantly by the transfer of a neutron -a two-step process. The prompt breakup probabilities are shown to have an exponential dependence on the surface-to-surface separation of the interacting nuclei, but are independent of the target nuclei, ranging from 144 Sm to 209 Bi . These results provide significant input towards a complete quantal model aiming to describe the breakup of weakly bound stable and halo nuclei.

Exponential dichotomies with respect to a sequence of norms and admissibility

2014 ◽  
Vol 25 (03) ◽  
pp. 1450024 ◽  
Author(s):  
Luis Barreira ◽  
Davor Dragičević ◽  
Claudia Valls
Keyword(s):  
Exponential Dichotomy ◽  
Linear Operators ◽  
Conditional Stability ◽  
Exponential Behavior ◽  
Exponential Dichotomies ◽  
Linear Perturbations ◽  
Nonuniform Exponential Dichotomy

For a nonautonomous dynamics defined by a sequence of linear operators, we introduce the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility in lp spaces, both for the space of perturbations and the space of solutions. This allows unifying the notions of uniform and nonuniform exponential behavior. Moreover, we consider the general case of a noninvertible dynamics. As a nontrivial application we show that the conditional stability of a nonuniform exponential dichotomy persists under sufficiently small linear perturbations.

scholarly journals Permanence of nonuniform nonautonomous hyperbolicity for infinite-dimensional differential equations

2021 ◽  
pp. 1-27
Author(s):  
Tomás Caraballo ◽  
Alexandre N. Carvalho ◽  
José A. Langa ◽  
Alexandre N. Oliveira-Sousa
Keyword(s):  
Differential Equations ◽  
Continuous Dependence ◽  
Exponential Dichotomy ◽  
Nonlinear Evolution ◽  
Nonuniform Hyperbolicity ◽  
Exponential Dichotomies ◽  
Infinite Dimensional ◽  
Linear Evolution ◽  
Nonuniform Exponential Dichotomies ◽  
Nonuniform Exponential Dichotomy

In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness result of nonuniform hyperbolicity for linear evolution processes, that is, we show that the property of admitting a nonuniform exponential dichotomy is stable under perturbation. Moreover, we provide conditions to obtain uniqueness and continuous dependence of projections associated with nonuniform exponential dichotomies. We also present an example of evolution process in a Banach space that admits nonuniform exponential dichotomy and study the permanence of the nonuniform hyperbolicity under perturbation. Finally, we prove persistence of nonuniform hyperbolic solutions for nonlinear evolution processes under perturbations.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

Characterization of CMOS Structures (0.6 µm process) Submitted to HBM and COM ESD Stress Tests

1997 ◽  
Author(s):  
G. Meneghesso ◽  
E. Zanoni ◽  
P. Colombo ◽  
M. Brambilla ◽  
R. Annunziata ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Electrostatic Discharge ◽  
Stress Test ◽  
Complete Characterization ◽  
Stress Tests ◽  
Test Procedures ◽  
Emission Microscopy ◽  
Fast Rise ◽  
Scanning Electron

Abstract In this work, we present new results concerning electrostatic discharge (ESD) robustness of 0.6 μm CMOS structures. Devices have been tested according to both HBM and socketed CDM (sCDM) ESD test procedures. Test structures have been submitted to a complete characterization consisting in: 1) measurement of the tum-on time of the protection structures submitted to pulses with very fast rise times; 2) ESD stress test with the HBM and sCDM models; 3) failure analysis based on emission microscopy (EMMI) and Scanning Electron Microscopy (SEM).

scholarly journals Complete characterization of spin chains with two Ising symmetries

2019 ◽  
Vol 125 (1) ◽  
pp. 10008 ◽  
Author(s):  
Bat-el Friedman ◽  
Atanu Rajak ◽  
Emanuele G. Dalla Torre
Keyword(s):  
Complete Characterization ◽  
Spin Chains
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