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Equi-attraction and continuity of attractors for skew-product semiflows
2016
Discrete and continuous dynamical systems. Series B
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In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, and equi-attraction and continuity of uniform and cocycle attractors associated ...
Results on the upper and lower-semicontinuity of uniform and cocycle attractors are relatively new in the literature, as a deep understanding of the internal structure of these sets is needed, which is ...
We would like to thank the referees for their helpful and interesting suggestions which allowed us to improve the presentation of the paper. ...
doi:10.3934/dcdsb.2016081
fatcat:huvsd2ebhrgjrpcndxinzu5ham
Page 528 of Mathematical Reviews Vol. 56, Issue 2
[page]
1978
Mathematical Reviews
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He does so, however, by introducing the idea of a semiflow associated with a process. ...
Lysko (Warsaw) Dafermos, Constantine M. 3813 Semiflows associated with and uniform
Math. Systems Theory 8 (1974/75), no. 2, 142-149. ...
Non-autonomous dynamical systems
2015
Discrete and continuous dynamical systems. Series B
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This fact leads to the definition of concepts such as skew-products and cocycles and their associated global, uniform, and cocycle attractors. ...
topological structural stability for the pullback attractors of evolution processes that arise from small non-autonomous perturbations, with respect to the limit regime. ...
Suppose Σ is compact and A(·) is the cocycle attractor of (ϕ, θ) and that Π(·) is the associated skew-product semiflow. ...
doi:10.3934/dcdsb.2015.20.703
fatcat:65bukdbeq5dihcrbeqsqtwsldm
Attractors for impulsive non-autonomous dynamical systems and their relations
2017
Journal of Differential Equations
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of asymptotic dynamics, such as the cocycle attractor, the uniform attractor and the global attractor for the impulsive skew-product semiflow. ...
Lastly, we illustrate our theory by exhibiting an example of a non-classical non-autonomous parabolic equation with subcritical nonlinearity and impulses. ...
we consider the impulsive skew-product semiflow associated with rpϕ, θq pX,Σq , M, Is, then we obtain the same object as if we first constructed the skew-product semiflow tΠptq : t ě 0u associated with ...
doi:10.1016/j.jde.2016.11.036
fatcat:2wvjiwcv5rfdjgbs6r76soig6q
Skew product semiflows and Morse decomposition
2013
Journal of Differential Equations
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In particular, we derive a Morse decomposition for the global attractors of skew product semiflows (and thus for pullback attractors of non-autonomous differential equations) from a Morse decomposition ...
The description of the asymptotic dynamics of non-autonomous equations lies on dynamical structures of some associated limiting non-autonomous -and autonomous -differential equations (one for each global ...
We would like to thank the referee for the helpful and interesting suggestions and comments which allowed us to significantly improve the presentation of this paper. ...
doi:10.1016/j.jde.2013.06.023
fatcat:444qjec4a5exxmkgtmegdw2wmy
On the uniform exponential stability of linear skew-product semiflows
2006
Journal of Function Spaces and Applications
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The problem of uniform exponential stability of linear skew-product semiflows on locally compact metric space with Banach fibers, is discussed. ...
It is established a connection between the uniform exponential stability of linear skewproduct semiflows and some admissibility-type condition. ...
We are setting an connection between the uniform exponential stability of a linear skew-product semiflow on a locally compact metric space and the admissibility of a function space from a large class of ...
doi:10.1155/2006/703620
fatcat:dkp4ard33fdudl7tu6uu7oivg4
Local Approximate Forward Attractors of Nonautonomous Dynamical Systems
2020
American Journal of Applied Mathematics
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Specifically, let φ be a cocycle semiflow on a Banach space X with driving system θ on a base space P . Suppose that the base space P is compact and φ is uniformly asymptotically compact. ...
Let A(·) be a local pullback attractor with p∈P A(p) being compact. ...
Based on the compactness of the base spaces, the pullback attraction of cocycle semiflow and (forward) attraction of the associated autonomous semiflow is shown to be equivalent. ...
doi:10.11648/j.ajam.20200805.16
fatcat:eysuipyryjgcxmzsnok75afkgm
The ODE method for some self-interacting diffusions on ℝ d
2010
Annales de l'I.H.P. Probabilites et statistiques
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These processes have so far been studied on compact spaces by Benaïm, Ledoux and Raimond, using stochastic approximation methods. ...
These are solutions to SDEs with a drift term depending on the actual position of the process and its normalized occupation measure µt. ...
, the deterministic semiflow associated to the self-interacting diffusion and show its local existence. The proofs of the main results are given in Section ?? ...
doi:10.1214/09-aihp206
fatcat:ivfaxdhqi5frzaw65filecgwwq
Uniform and strict persistence in monotone skew-product semiflows with applications to non-autonomous Nicholson systems
2016
Journal of Differential Equations
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in terms of the principal spectrums of some associated linear skew-product semiflows which admit a continuous separation. ...
We determine sufficient conditions for uniform and strict persistence in the case of skew-product semiflows generated by solutions of nonautonomous families of cooperative systems of ODEs or delay FDEs ...
Uniform and strict persistence in abstract monotone skew-product semiflows with a continuous separation In this section, we analyze the notions of uniform and strict persistence in a very general context ...
doi:10.1016/j.jde.2016.06.019
fatcat:v6b5ok2oyjhx7cduhwjnvuarku
Page 7810 of Mathematical Reviews Vol. , Issue 2004j
[page]
2004
Mathematical Reviews
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Then they prove that the uniform exponen- tial dichotomy of a linear skew-product semiflow is equivalent to the uniform exponential dichotomy of the associated discrete linear skew-product semiflow. ...
Based on results of Chow and Leiva and of Latushkin and Schnaubelt, the authors discuss the connections between the uniform exponential dichotomy of a discrete linear skew- product semiflow and the uniform ...
Compactifications of Dynamical Systems
[article]
2010
arXiv
pre-print
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In the process we don't want to introduce recurrence which was not there in the original system. ...
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. ...
Let φ be a semiflow on X and letX be a proper compactification with inclusion map j : X →X and associated algebra A = j * (B(X)) ⊂ B(X). ...
arXiv:1004.0323v1
fatcat:ihnwrom4qrejlp7senlai5dq7i
A generalized Polya's urn with graph based interactions
[article]
2013
arXiv
pre-print
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We also prove that if a<1 then there is a single point v=v(G,a) with nonzero entries such that the proportion converges to v almost surely. A special case is when G is regular and a is at most 1. ...
We show e.g. that if G is non-bipartite then the proportion of balls in the bins converges to the uniform measure almost surely. ...
Acknowledgements The authors are thankful to Omer Angel and Omri Sarig for valuable comments and suggestions. I.B. is the incumbent of the Renee and Jay Weiss Professorial Chair. ...
arXiv:1211.1247v4
fatcat:j25o24fzdfeflcxwjixsjetpje
Non-autonomous perturbations of a non-classical non-autonomous parabolic equation with subcritical nonlinearity
2017
Applied Mathematics and Nonlinear Sciences
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Dealing with perturbations adds a difficulty to this process, since we must be able to do such study for each ε small and obtain the result with uniformity in this parameter. ...
A NDS (ϕ, σ ) (X,Σ) has a uniform attractor if and only if there exists a compact uniform attracting set K. ...
Moreover, for 0 ε ε 1 , we have With this result, we can derive structures for the other types of attractors, as we did for A 0 ; namely, we have that the uniform attractor of (ϕ ε , θ ) (H 1 0 (Ω),Σ ε ...
doi:10.21042/amns.2017.1.00004
fatcat:u4yj7vwewfakzlhw7y5b6jbbfq
Minimality properties of set-valued processes and their pullback attractors
[article]
2014
arXiv
pre-print
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The presentation is complemented with examples and counterexamples to test the sharpness of the hypotheses involved, including a reaction-diffusion equation, a discontinuous ordinary differential equation ...
and an irregular form of the heat equation. ...
Global attractors for m-semiflows. Observe that an m-semiflow is asymptoti-
cally compact if and only if the associated m-process is pullback asymptotically compact. ...
arXiv:1407.6135v2
fatcat:w7vd4yhkm5bq3ova32qahqpp5q
On Exponential Stability for Skew-Evolution Semiflows on Banach Spaces
[article]
2008
arXiv
pre-print
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The paper emphasizes the property of stability for skew-evolution semiflows on Banach spaces, defined by means of evolution semiflows and evolution cocycles and which generalize the concept introduced ...
A unified treatment in the uniform and in the nonuniform setting is given. The main results are also formulated in discrete time. ...
Let us consider the set C = C(R, R) of all continuous functions given by x : R → R, endowed with the uniform convergence topology on compact subsets of R. ...
arXiv:0804.1479v1
fatcat:6d5dbvvnrrendaflgkgjecnt3e
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