Displaying similar documents to “Global attractors for a tropical climate model”

Global Attractor for the Convective Cahn-Hilliard Equation

Xiaopeng Zhao, Changchun Liu (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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This paper is concerned with the convective Cahn-Hilliard equation. We use a classical theorem on existence of a global attractor to derive that the convective Cahn-Hilliard equation possesses a global attractor on some subset of H².

On the Hausdorff dimension of a family of self-similar sets with complicated overlaps

Balázs Bárány (2009)

Fundamenta Mathematicae

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We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...

On the attractors of Feigenbaum maps

Guifeng Huang, Lidong Wang (2014)

Annales Polonici Mathematici

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A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every s ∈ (0,1), we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is s.

Remarks on the Fractal Dimension of Bi-Space Global and Exponential Attractors

Jan W. Cholewa, Radoslaw Czaja, Gianluca Mola (2008)

Bollettino dell'Unione Matematica Italiana

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Bi-space global and exponential attractors for the time continuous dynamical systems are considered and the bounds on their fractal dimension are discussed in the context of the smoothing properties of the system between appropriately chosen function spaces. The case when the system exhibits merely some partial smoothing properties is also considered and applications to the sample problems are given.

On the definition of strange nonchaotic attractor

Lluís Alsedà, Sara Costa (2009)

Fundamenta Mathematicae

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The aim of this paper is twofold. On the one hand, we want to discuss some methodological issues related to the notion of strange nonchaotic attractor. On the other hand, we want to formulate a precise definition of this kind of attractor, which is "observable" in the physical sense and, in the two-dimensional setting, includes the well known models proposed by Grebogi et al. and by Keller, and a wide range of other examples proposed in the literature. Furthermore, we analytically prove...

Some models of Cahn-Hilliard equations in nonisotropic media

Alain Miranville (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We derive in this article some models of Cahn-Hilliard equations in nonisotropic media. These models, based on constitutive equations introduced by Gurtin in [19], take the work of internal microforces and also the deformations of the material into account. We then study the existence and uniqueness of solutions and obtain the existence of finite dimensional attractors.

Compact Global Chaotic Attractors of Discrete Control Systems

David Cheban (2014)

Nonautonomous Dynamical Systems

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The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fν(n)(xn), where ν : ℤ+ ⃗ {1,2,...,m}. If m ≥ 2 we give sufficient conditions (the family M := {f1,f2,...,fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework...

A note on LaSalle's problems

Anna Cima, Armengol Gasull, Francesc Mañosas (2001)

Annales Polonici Mathematici

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In LaSalle's book "The Stability of Dynamical Systems", the author gives four conditions which imply that the origin of a discrete dynamical system defined on ℝ is a global attractor, and proposes to study the natural extensions of these conditions in ℝⁿ. Although some partial results are obtained in previous papers, as far as we know, the problem is not completely settled. In this work we first study the four conditions and prove that just one of them implies that the origin is a global...

On the viscous Allen-Cahn and Cahn-Hilliard systems with Willmore regularization

Ahmad Makki (2016)

Applications of Mathematics

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We consider the viscous Allen-Cahn and Cahn-Hilliard models with an additional term called the nonlinear Willmore regularization. First, we are interested in the well-posedness of these two models. Furthermore, we prove that both models possess a global attractor. In addition, as far as the viscous Allen-Cahn equation is concerned, we construct a robust family of exponential attractors, i.e. attractors which are continuous with respect to the perturbation parameter. Finally, we give...