The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Claudia Valls - One of the best experts on this subject based on the ideXlab platform.
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Stable manifolds for perturbations of exponential dichotomies in mean
Stochastics and Dynamics, 2017Co-Authors: Luis Barreira, Claudia VallsAbstract:We establish the existence of stable invariant manifolds for any sufficiently small perturbation of a cocycle with an exponential Dichotomy in mean. The latter notion corresponds to replace the exponential behavior in the classical notion of an exponential Dichotomy by an exponential behavior in average with respect to an invariant measure. We consider both perturbations of a cocycle over a map and over a flow that can be defined on an arbitrary Banach space. Moreover, we obtain an upper bound for the speed of the nonlinear dynamics along the stable manifold as well as a lower bound when the exponential Dichotomy in mean is strong (this means that we have lower and upper bounds along the stable and unstable directions of the Dichotomy).
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Fredholm operators and nonuniform exponential dichotomies
Chaos Solitons & Fractals, 2016Co-Authors: Luis Barreira, Davor Dragičević, Claudia VallsAbstract:Abstract We show that the existence of a nonuniform exponential Dichotomy for a one-sided sequence (Am)m ≥ 0 of invertible d × d matrices is equivalent to the Fredholm property of a certain linear operator between spaces of bounded sequences. Moreover, for a two-sided sequence ( A m ) m ∈ Z we show that the existence of a nonuniform exponential Dichotomy implies that a related operator S is Fredholm and that if it is Fredholm, then the sequence admits nonuniform exponential dichotomies on Z 0 + and Z 0 − . We also give conditions on S so that the sequence admits a nonuniform exponential Dichotomy on Z . Finally, we use the former characterizations to establish the robustness of the notion of a nonuniform exponential Dichotomy.
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From one-sided dichotomies to two-sided dichotomies
Discrete & Continuous Dynamical Systems - A, 2015Co-Authors: Luis Barreira, Davor Dragičević, Claudia VallsAbstract:For a general nonautonomous dynamics on a Banach space, we give a necessary and sufficient condition so that the existence of one-sided exponential dichotomies on the past and on the future gives rise to a two-sided exponential Dichotomy. The condition is that the stable space of the future at the origin and the unstable space of the past at the origin generate the whole space. We consider the general cases of a noninvertible dynamics as well as of a nonuniform exponential Dichotomy and a strong nonuniform exponential Dichotomy (for the latter, besides the requirements for a nonuniform exponential Dichotomy we need to have a minimal contraction and a maximal expansion). Both notions are ubiquitous in ergodic theory. Our approach consists in reducing the study of the dynamics to one with uniform exponential behavior with respect to a family of norms and then using the characterization of uniform hyperbolicity in terms of an admissibility property in order to show that the dynamics admits a two-sided exponential Dichotomy. As an application, we give a complete characterization of the set of Lyapunov exponents of a Lyapunov regular dynamics, in an analogous manner to that in the Sacker--Sell theory.
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Noninvertible cocycles: Robustness of exponential dichotomies
Discrete and Continuous Dynamical Systems, 2012Co-Authors: Luis Barreira, Claudia VallsAbstract:For the dynamics defined by a sequence of bounded linear operators in a Banach space, we establish the robustness of the notion of exponential Dichotomy. This means that an exponential Dichotomy persists under sufficiently small linear perturbations. We consider the general cases of a nonuniform exponential Dichotomy, which requires much less than a uniform exponential Dichotomy, and of a noninvertible dynamics or, more precisely, of a dynamics that may not be invertible in the stable direction.
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Stability of dichotomies in difference equations with infinite delay
Nonlinear Analysis: Theory Methods & Applications, 2010Co-Authors: Luis Barreira, Claudia VallsAbstract:Abstract For delay difference equations with infinite delay we consider the notion of nonuniform exponential Dichotomy. This includes the notion of uniform exponential Dichotomy as a very special case. Our main aim is to establish a stable manifold theorem under sufficiently small nonlinear perturbations. We also establish the robustness of nonuniform exponential dichotomies under sufficiently small linear perturbations. Finally, we characterize the nonuniform exponential dichotomies in terms of strict Lyapunov sequences. In particular, we construct explicitly a strict Lyapunov sequence for each exponential Dichotomy.
Farahnaz Faez - One of the best experts on this subject based on the ideXlab platform.
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reconceptualizing the native nonnative speaker Dichotomy
Journal of Language Identity and Education, 2011Co-Authors: Farahnaz FaezAbstract:This study reconceptualizes the native/nonnative Dichotomy and provides a powerful lens to examine linguistic identities. In a study of 25 linguistically diverse teacher candidates in Canada, the respondents' native and nonnative self-ascription and self-assessed level of proficiency was juxtaposed with the judgment of their instructors. This process revealed that the native/nonnative Dichotomy falls short in capturing the multifaceted nature of individuals' diverse linguistic identities and tends to misrepresent them. Within the specific social context under investigation, 6 linguistic categories that better represented the true linguistic identity of participants were identified. This inquiry reconceptualizes the controversial native/nonnative Dichotomy by suggesting that linguistic identities should be viewed using a sociocultural lens whereby the dynamic, dialogic, multiple, and situated nature of identity is emphasized. The reconceptualization of the native/nonnative Dichotomy indicates that individu...
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Reconceptualizing the Native/Nonnative Speaker Dichotomy
Journal of Language Identity & Education, 2011Co-Authors: Farahnaz FaezAbstract:This study reconceptualizes the native/nonnative Dichotomy and provides a powerful lens to examine linguistic identities. In a study of 25 linguistically diverse teacher candidates in Canada, the respondents' native and nonnative self-ascription and self-assessed level of proficiency was juxtaposed with the judgment of their instructors. This process revealed that the native/nonnative Dichotomy falls short in capturing the multifaceted nature of individuals' diverse linguistic identities and tends to misrepresent them. Within the specific social context under investigation, 6 linguistic categories that better represented the true linguistic identity of participants were identified. This inquiry reconceptualizes the controversial native/nonnative Dichotomy by suggesting that linguistic identities should be viewed using a sociocultural lens whereby the dynamic, dialogic, multiple, and situated nature of identity is emphasized. The reconceptualization of the native/nonnative Dichotomy indicates that individu...
Linda S Adair - One of the best experts on this subject based on the ideXlab platform.
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quantifying the urban environment a scale measure of urbanicity outperforms the urban rural Dichotomy
Social Science & Medicine, 2007Co-Authors: Darren Dahly, Linda S AdairAbstract:The rapid urbanization of the developing world has important consequences for human health. Although several authorities have called for better research on the relationships between urbanicity and health, most researchers still use a poor measurement of urbanicity, the urban-rural Dichotomy. Our goal was to construct a scale of urbanicity using community level data from the Cebu Longitudinal Health and Nutrition Survey. We used established scale development methods to validate the new measure and tested its performance against the Dichotomy. The new scale illustrated misclassification by the urban-rural Dichotomy, and was able to detect differences in urbanicity, both between communities and across time, that were not apparent before. Furthermore, using a continuous measure of urbanicity allowed for better illustrations of the relationships between urbanicity and health. The new scale is a better measure of urbanicity than the traditionally used urban-rural Dichotomy.
Ronald C Nyhan - One of the best experts on this subject based on the ideXlab platform.
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the politics administration Dichotomy an empirical search for correspondence between theory and practice
Public Administration Review, 2008Co-Authors: Tansu Demir, Ronald C NyhanAbstract:The politics–administration Dichotomy has been one of the most disputed theories of public administration. Despite serious critiques, neither the theoretical utility nor the normative power of the Dichotomy has totally disappeared over the past decades. The Dichotomy has been advocated on the grounds that the dichotomous division of labor and authority between elected and administrative officials increases the democratic accountability and planning ability of public administrators. This article first builds a theoretical model of the politics–administration Dichotomy and then evaluates the model using empirical data collected from a nationwide sample of city managers serving in council-manager local governments. Results of structural equation modeling illustrate that the politics–administration Dichotomy fails to obtain its predicted tendencies in actuality. The authors interpret the findings in light of the contemporary public administration literature. The article aims to make a theoretical-empirical contribution to one of the most challenging questions in public administration.
Luis Barreira - One of the best experts on this subject based on the ideXlab platform.
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Stable manifolds for perturbations of exponential dichotomies in mean
Stochastics and Dynamics, 2017Co-Authors: Luis Barreira, Claudia VallsAbstract:We establish the existence of stable invariant manifolds for any sufficiently small perturbation of a cocycle with an exponential Dichotomy in mean. The latter notion corresponds to replace the exponential behavior in the classical notion of an exponential Dichotomy by an exponential behavior in average with respect to an invariant measure. We consider both perturbations of a cocycle over a map and over a flow that can be defined on an arbitrary Banach space. Moreover, we obtain an upper bound for the speed of the nonlinear dynamics along the stable manifold as well as a lower bound when the exponential Dichotomy in mean is strong (this means that we have lower and upper bounds along the stable and unstable directions of the Dichotomy).
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Fredholm operators and nonuniform exponential dichotomies
Chaos Solitons & Fractals, 2016Co-Authors: Luis Barreira, Davor Dragičević, Claudia VallsAbstract:Abstract We show that the existence of a nonuniform exponential Dichotomy for a one-sided sequence (Am)m ≥ 0 of invertible d × d matrices is equivalent to the Fredholm property of a certain linear operator between spaces of bounded sequences. Moreover, for a two-sided sequence ( A m ) m ∈ Z we show that the existence of a nonuniform exponential Dichotomy implies that a related operator S is Fredholm and that if it is Fredholm, then the sequence admits nonuniform exponential dichotomies on Z 0 + and Z 0 − . We also give conditions on S so that the sequence admits a nonuniform exponential Dichotomy on Z . Finally, we use the former characterizations to establish the robustness of the notion of a nonuniform exponential Dichotomy.
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From one-sided dichotomies to two-sided dichotomies
Discrete & Continuous Dynamical Systems - A, 2015Co-Authors: Luis Barreira, Davor Dragičević, Claudia VallsAbstract:For a general nonautonomous dynamics on a Banach space, we give a necessary and sufficient condition so that the existence of one-sided exponential dichotomies on the past and on the future gives rise to a two-sided exponential Dichotomy. The condition is that the stable space of the future at the origin and the unstable space of the past at the origin generate the whole space. We consider the general cases of a noninvertible dynamics as well as of a nonuniform exponential Dichotomy and a strong nonuniform exponential Dichotomy (for the latter, besides the requirements for a nonuniform exponential Dichotomy we need to have a minimal contraction and a maximal expansion). Both notions are ubiquitous in ergodic theory. Our approach consists in reducing the study of the dynamics to one with uniform exponential behavior with respect to a family of norms and then using the characterization of uniform hyperbolicity in terms of an admissibility property in order to show that the dynamics admits a two-sided exponential Dichotomy. As an application, we give a complete characterization of the set of Lyapunov exponents of a Lyapunov regular dynamics, in an analogous manner to that in the Sacker--Sell theory.
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Noninvertible cocycles: Robustness of exponential dichotomies
Discrete and Continuous Dynamical Systems, 2012Co-Authors: Luis Barreira, Claudia VallsAbstract:For the dynamics defined by a sequence of bounded linear operators in a Banach space, we establish the robustness of the notion of exponential Dichotomy. This means that an exponential Dichotomy persists under sufficiently small linear perturbations. We consider the general cases of a nonuniform exponential Dichotomy, which requires much less than a uniform exponential Dichotomy, and of a noninvertible dynamics or, more precisely, of a dynamics that may not be invertible in the stable direction.
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Stability of dichotomies in difference equations with infinite delay
Nonlinear Analysis: Theory Methods & Applications, 2010Co-Authors: Luis Barreira, Claudia VallsAbstract:Abstract For delay difference equations with infinite delay we consider the notion of nonuniform exponential Dichotomy. This includes the notion of uniform exponential Dichotomy as a very special case. Our main aim is to establish a stable manifold theorem under sufficiently small nonlinear perturbations. We also establish the robustness of nonuniform exponential dichotomies under sufficiently small linear perturbations. Finally, we characterize the nonuniform exponential dichotomies in terms of strict Lyapunov sequences. In particular, we construct explicitly a strict Lyapunov sequence for each exponential Dichotomy.
