The Experts below are selected from a list of 5985 Experts worldwide ranked by ideXlab platform
Ian Melbourne - One of the best experts on this subject based on the ideXlab platform.
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Correction to: A note on diffusion limits of chaotic Skew-Product flows
2020Co-Authors: Ian Melbourne, Andrew StuartAbstract:Abstract This fixes a gap in the averaging argument in our paper: A note on diffusion limits of chaotic Skew Product flows. Nonlinearity (2011) 1361-1367, and moreover shows that the large deviation estimate assumed there is redundant. , but the proof is incorrect. Specifically, the proof introduces a random variable J n (see below) that depends on x ( ) (n 3/2 ) and y (1) (s), and derives an estimate for E|J n |. This estimate takes into account the randomness of y (1) (s) but overlooks the randomness of x ( ) (n 3/2 ). In this note, we correct the argument in Proof Following the calculation in [2, Section 3] with δ = 3/2 , we obtain ma
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exponential decay of correlations for nonuniformly hyperbolic flows with a c 1 alpha c 1 α stable foliation including the classical lorenz attractor
Annales Henri Poincaré, 2016Co-Authors: Vitor Araujo, Ian MelbourneAbstract:We prove exponential decay of correlations for a class of \({C^{1+\alpha}}\) uniformly hyperbolic Skew Product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open set of geometric Lorenz attractors. As a special case, we show that the classical Lorenz attractor is robustly exponentially mixing.
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exponential decay of correlations for nonuniformly hyperbolic flows with a c 1 alpha stable foliation
arXiv: Dynamical Systems, 2015Co-Authors: Vitor Araujo, Ian MelbourneAbstract:We prove exponential decay of correlations for a class of C^{1+\alpha} uniformly hyperbolic Skew Product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open and dense set of geometric Lorenz attractors in a neighborhood of the classical Lorenz attractor.
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exponential decay of correlations for nonuniformly hyperbolic flows with a c 1 alpha stable foliation including the classical lorenz attractor
arXiv: Dynamical Systems, 2015Co-Authors: Vitor Araujo, Ian MelbourneAbstract:We prove exponential decay of correlations for a class of $C^{1+\alpha}$ uniformly hyperbolic Skew Product flows, subject to a uniform nonintegrability condition. In particular, this establishes exponential decay of correlations for an open set of geometric Lorenz attractors. As a special case, we show that the classical Lorenz attractor is robustly exponentially mixing.
Zhi-cheng Wang - One of the best experts on this subject based on the ideXlab platform.
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Exponential dichotomy and admissibility of linearized Skew-Product semiflows defined on a compact positively invariant subset of semiflows
Nonlinear Analysis: Real World Applications, 2009Co-Authors: Bin-guo Wang, Zhi-cheng WangAbstract:Abstract We study exponential dichotomy of linear Skew-Product semiflows which come from linearizing Skew-Product semiflows on a compact positively invariant subset M of semiflows and construct the relationship between continuous separation and exponential dichotomy under assumptions that Skew-Product semiflows are eventually strongly monotone. In addition, we deduce that the exponential dichotomy is trivial when M is hyperbolically stable, and the hyperbolic instability of M is the necessary condition of the state space admitting a trivial separation in another forms. Simultaneously, we list some conditions for hyperbolic stability and instability of M . At last, we construct a sufficient and necessary condition for exponential dichotomy of linear Skew-Product semiflows in terms of the admissibility of the pair ( B ( R + , X ) , B 0 ( R + , X ) ) .
Stephan Lawi - One of the best experts on this subject based on the ideXlab platform.
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towards a characterization of markov processes enjoying the time inversion property
Journal of Theoretical Probability, 2008Co-Authors: Stephan LawiAbstract:We give a necessary and sufficient condition for a homogeneous Markov process taking values in ℝn to enjoy the time-inversion property of degree α. The condition sets the shape for the semigroup densities of the process and allows to further extend the class of known processes satisfying the time-inversion property. As an application we recover the result of Watanabe (Z. Wahrscheinlichkeitstheor. Verwandte Geb. 31:115–124, 1975) for continuous and conservative Markov processes on ℝ+. As new examples we generalize Dunkl processes and construct a matrix-valued process with jumps related to the Wishart process by a Skew-Product representation.
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towards a characterization of markov processes enjoying the time inversion property
arXiv: Probability, 2005Co-Authors: Stephan LawiAbstract:We give a necessary and sufficient condition for a homogeneous Markov process taking values in $\R^n$ to enjoy the time-inversion property of degree $\alpha$. The condition sets the shape for the semigroup densities of the process and allows to further extend the class of known processes satisfying the time-inversion property. As an application we recover the result of Watanabe in \cite{Wa1975} for continuous and conservative Markov processes on $\R_+$. As new examples we generalize Dunkl processes and construct a matrix-valued process with jumps related to the Wishart process by a Skew-Product representation.
Yonatan Gutman - One of the best experts on this subject based on the ideXlab platform.
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a juzvinskii addition theorem for finitely generated free group actions
Ergodic Theory and Dynamical Systems, 2014Co-Authors: Lewis Bowen, Yonatan GutmanAbstract:The classical Juzvinskii addition theorem states that the entropy of an automorphism of a compact group decomposes along invariant subgroups. Thomas generalized the theorem to a Skew-Product setting. Using L. Bowen’s f-invariant , we prove the addition theorem for actions of finitely generated free groups on Skew-Products with compact totally disconnected groups or compact Lie groups (correcting an error in L. Bowen [Nonabelian free group actions: Markov processes, the Abramov–Rohlin formula and Yuzvinskii’s formula. Ergod. Th. & Dynam. Sys. 30 (6) (2010), 1629–1663]) and discuss examples.
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a juzvinski u i addition theorem for finitely generated free groups actions
arXiv: Dynamical Systems, 2011Co-Authors: Lewis Bowen, Yonatan GutmanAbstract:The classical Juzvinski\u{i} Addition Theorem states that the entropy of an automorphism of a compact group decomposes along invariant subgroups. Thomas generalized the theorem to a Skew-Product setting. Using L. Bowen's f-invariant we prove the addition theorem for actions of finitely generated free groups on Skew-Products with compact totally disconnected groups or compact Lie groups (correcting an error from [Bo10c]) and discuss examples.
Yi Wang - One of the best experts on this subject based on the ideXlab platform.
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Almost automorphically forced flows on $S^1$ or $\mathbb{R}$ in one-dimensional almost periodic semilinear heat equations
2020Co-Authors: Shen Wenxian, Yi Wang, Zhou DunAbstract:In this paper, we consider the asymptotic dynamics of the Skew-Product semiflow generated by the following time almost-periodically forced scalar reaction-diffusion equation \begin{equation}\label{eq0} u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\, 0
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Phase-translation group actions on strongly monotone Skew-Product semiflows
Transactions of the American Mathematical Society, 2012Co-Authors: Yi WangAbstract:We establish a convergence property for pseudo-bounded forward orbits of strongly monotone Skew-Product semiflows with invariant phasetranslation group actions. The results are then applied to obtain global convergence of certain chemical reaction networks whose associated systems in reaction coordinates are monotone, as well as the dynamics of certain reactiondiffusion systems in time-recurrent structure including periodicity, almost periodicity and almost automorphy.
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Asymptotic symmetry in strongly monotone Skew-Product semiflows with applications
Nonlinearity, 2009Co-Authors: Yi WangAbstract:For strongly monotone Skew-Product semiflows on which a compact connected group acts, it is shown that any stable minimal set is residually symmetric and any uniformly stable trajectory is asymptotically symmetric. These results are then applied to study the spatio-temporal asymptotics of stable solutions of reaction–diffusion equations on a symmetric domain in time-recurrent structures including almost periodicity. In particular, the 1-covering property of omega-limit sets is established for uniformly stable bounded solutions of reaction–diffusion equations on a ball.