Flows near compact invariant sets. Part I

Pedro Teixeira

Displaying similar documents to “Flows near compact invariant sets. Part I”

Multiple disjointness and invariant measures on minimal distal flows

Juho Rautio (2015)

Studia Mathematica

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We examine multiple disjointness of minimal flows, that is, we find conditions under which the product of a collection of minimal flows is itself minimal. Our main theorem states that, for a collection ${X_{i}}_{i \in I}$ of minimal flows with a common phase group, assuming each flow satisfies certain structural and algebraic conditions, the product $\prod_{i \in I} X_{i}$ is minimal if and only if $\prod_{i \in I} X_{i}^{e q}$ is minimal, where $X_{i}^{e q}$ is the maximal equicontinuous factor of $X_{i}$ . Most importantly, this result holds when each $X_{i}$ is distal. When...

An attraction result and an index theorem for continuous flows on $ℝ^{n} \times [0, \infty)$

Klaudiusz Wójcik (1997)

Annales Polonici Mathematici

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We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on $E = ℝ^{n + 1}$ for which $\partial E = ℝ^{n} \times 0$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in EE such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^{n} \times [0, \infty)$ .

Polynomial decay of correlations for a class of smooth flows on the two torus

Bassam Fayad (2001)

Bulletin de la Société Mathématique de France

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Kočergin introduced in 1975 a class of smooth flows on the two torus that are mixing. When these flows have one fixed point, they can be viewed as special flows over an irrational rotation of the circle, with a ceiling function having a power-like singularity. Under a Diophantine condition on the rotation’s angle, we prove that the special flows actually have a $t^{- η}$ -speed of mixing, for some $η > 0$ .

On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. Leitman, Epifanio G. Virga (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function $G$ is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming $G$ to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial. ...

On embeddability of automorphisms into measurable flows from the point of view of self-joining properties

Joanna Kułaga-Przymus (2015)

Fundamenta Mathematicae

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We compare self-joining and embeddability properties. In particular, we prove that a measure preserving flow ${(T_{t})}_{t \in ℝ}$ with T₁ ergodic is 2-fold quasi-simple (resp. 2-fold distally simple) if and only if T₁ is 2-fold quasi-simple (resp. 2-fold distally simple). We also show that the Furstenberg-Zimmer decomposition for a flow ${(T_{t})}_{t \in ℝ}$ with T₁ ergodic with respect to any flow factor is the same for ${(T_{t})}_{t \in ℝ}$ and for T₁. We give an example of a 2-fold quasi-simple flow disjoint from simple flows and whose time-one...

On new characterization of inextensible flows of space-like curves in de Sitter space

Mustafa Yeneroğlu (2016)

Open Mathematics

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Elastica and inextensible flows of curves play an important role in practical applications. In this paper, we construct a new characterization of inextensible flows by using elastica in space. The inextensible flow is completely determined for any space-like curve in de Sitter space [...] S 1 3 $𝕊_{1}^{3}$ . Finally, we give some characterizations for curvatures of a space-like curve in de Sitter space [...] S 1 3 $𝕊_{1}^{3}$ .

Topological dynamics of unordered Ramsey structures

Moritz Müller, András Pongrácz (2015)

Fundamenta Mathematicae

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We investigate the connections between Ramsey properties of Fraïssé classes and the universal minimal flow $M (G_{)}$ of the automorphism group $G$ of their Fraïssé limits. As an extension of a result of Kechris, Pestov and Todorcevic (2005) we show that if the class has finite Ramsey degree for embeddings, then this degree equals the size of $M (G_{)}$ . We give a partial answer to a question of Angel, Kechris and Lyons (2014) showing that if is a relational Ramsey class and $G$ is amenable, then $M (G_{)}$ admits...

Amenability and unique ergodicity of automorphism groups of Fraïssé structures

Andy Zucker (2014)

Fundamenta Mathematicae

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In this paper we consider those Fraïssé classes which admit companion classes in the sense of [KPT]. We find a necessary and sufficient condition for the automorphism group of the Fraïssé limit to be amenable and apply it to prove the non-amenability of the automorphism groups of the directed graph S(3) and the boron tree structure T. Also, we provide a negative answer to the Unique Ergodicity-Generic Point problem of Angel-Kechris-Lyons [AKL]. By considering $G L (V_{\infty})$ , where $V_{\infty}$ is the countably...

A map maintaining the orbits of a given $ℤ^{d}$ -action

Bartosz Frej, Agata Kwaśnicka (2016)

Colloquium Mathematicae

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Giordano et al. (2010) showed that every minimal free $ℤ^{d}$ -action of a Cantor space X is orbit equivalent to some ℤ-action. Trying to avoid the K-theory used there and modifying Forrest’s (2000) construction of a Bratteli diagram, we show how to define a (one-dimensional) continuous and injective map F on X∖one point such that for a residual subset of X the orbits of F are the same as the orbits of a given minimal free $ℤ^{d}$ -action.

On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. Leitman, Epifanio G. Virga (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Minimal systems and distributionally scrambled sets

Piotr Oprocha (2012)

Bulletin de la Société Mathématique de France

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In this paper we investigate numerous constructions of minimal systems from the point of view of $(ℱ_{1}, ℱ_{2})$ -chaos (but most of our results concern the particular cases of distributional chaos of type $1$ and $2$ ). We consider standard classes of systems, such as Toeplitz flows, Grillenberger $K$ -systems or Blanchard-Kwiatkowski extensions of the Chacón flow, proving that all of them are DC2. An example of DC1 minimal system with positive topological entropy is also introduced. The above mentioned results...

Generalized gradient flow and singularities of the Riemannian distance function

Piermarco Cannarsa (2012-2013)

Séminaire Laurent Schwartz — EDP et applications

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Significant information about the topology of a bounded domain $Ω$ of a Riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partial Ω}$ , from the boundary of $Ω$ . We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of $d_{\partial Ω}$ , as well as applications to homotopy equivalence.

Ricci flow coupled with harmonic map flow

Reto Müller (2012)

Annales scientifiques de l'École Normale Supérieure

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We investigate a coupled system of the Ricci flow on a closed manifold $M$ with the harmonic map flow of a map $φ$ from $M$ to some closed target manifold $N$ , $\frac{\partial}{\partial t} g = - 2 Rc + 2 α \nabla φ \otimes \nabla φ, \frac{\partial}{\partial t} φ = τ_{g} φ,$ where $α$ is a (possibly time-dependent) positive coupling constant. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of $φ$ a-priori by choosing $α$ large enough. Moreover, it suffices to bound the curvature...

Free convection flow of water at $4^{\circ} C$ past an infinite porous plate with constant suction

V. M. Soundalgekar (1975)

Matematički Vesnik

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The $n$ -centre problem of celestial mechanics for large energies

Andreas Knauf (2002)

Journal of the European Mathematical Society

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We consider the classical three-dimensional motion in a potential which is the sum of $n$ attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the $n$ centres, we find a universal behaviour for all energies $E$ above a positive threshold. Whereas for $n = 1$ there are no bounded orbits, and for $n = 2$ there is just one closed orbit, for $n \geq 3$ the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of...

On the Hausdorff Dimension of Topological Subspaces

Tomasz Szarek, Maciej Ślęczka (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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It is shown that every Polish space X with $d i m_{T} X \geq d$ admits a compact subspace Y such that $d i m_{H} Y \geq d$ where $d i m_{T}$ and $d i m_{H}$ denote the topological and Hausdorff dimensions, respectively.

Automatic continuity of operators commuting with translations

J. Alaminos, J. Extremera, A. R. Villena (2006)

Studia Mathematica

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Let $τ_{X}$ and $τ_{Y}$ be representations of a topological group G on Banach spaces X and Y, respectively. We investigate the continuity of the linear operators Φ: X → Y with the property that $Φ \circ τ_{X} (t) = τ_{Y} (t) \circ Φ$ for each t ∈ G in terms of the invariant vectors in Y and the automatic continuity of the invariant linear functionals on X.

A second order unconditionally positive space-time residual distribution method for solving compressible flows on moving meshes

Dobeš, Jiří, Deconinck, Herman

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A space-time formulation for unsteady inviscid compressible flow computations in 2D moving geometries is presented. The governing equations in Arbitrary Lagrangian-Eulerian formulation (ALE) are discretized on two layers of space-time finite elements connecting levels $n$ , $n + 1 / 2$ and $n + 1$ . The solution is approximated with linear variation in space (P1 triangle) combined with linear variation in time. The space-time residual from the lower layer of elements is distributed to the nodes at level...

Scattering for 1D cubic NLS and singular vortex dynamics

Valeria Banica, Luis Vega (2012)

Journal of the European Mathematical Society

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We study the stability of self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions $χ_{a} (t, x)$ form a family of evolving regular curves in $ℝ^{3}$ that develop a singularity in finite time, indexed by a parameter $a > 0$ . We consider curves that are small regular perturbations of $χ_{a} (t_{0}, x)$ for a fixed time $t_{0}$ . In particular, their curvature is not vanishing at infinity, so we are not in the context of known results of...

On invariant, dual invariant and absolute formulas

Andrzej Mostowski

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CONTENTS Introduction..............................................................................................................................................................3 1. Lemmas concerning first order formulas.....................................................................................................5 2. Representability of recursively enumerable sets........................................................................................9 3. Simple theory of types.......................................................................................................................................10...

Some model theory of SL(2,ℝ)

Jakub Gismatullin, Davide Penazzi, Anand Pillay (2015)

Fundamenta Mathematicae

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We study the action of G = SL(2,ℝ), viewed as a group definable in the structure M = (ℝ,+,×), on its type space $S_{G} (M)$ . We identify a minimal closed G-flow I and an idempotent r ∈ I (with respect to the Ellis semigroup structure * on $S_{G} (M)$ ). We also show that the “Ellis group” (r*I,*) is nontrivial, in fact it is the group with two elements, yielding a negative answer to a question of Newelski.

Monotonicity of first eigenvalues along the Yamabe flow

Liangdi Zhang (2021)

Czechoslovak Mathematical Journal

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We construct some nondecreasing quantities associated to the first eigenvalue of $- Δ_{φ} + c R$ $(c \geq \frac{1}{2} (n - 2) / (n - 1))$ along the Yamabe flow, where $Δ_{φ}$ is the Witten-Laplacian operator with a $C^{2}$ function $φ$ . We also prove a monotonic result on the first eigenvalue of $- Δ_{φ} + \frac{1}{4} (n / (n - 1)) R$ along the Yamabe flow. Moreover, we establish some nondecreasing quantities for the first eigenvalue of $- Δ_{φ} + c R^{a}$ with $a \in (0, 1)$ along the Yamabe flow.

Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle

Reinhard Farwig (2005)

Banach Center Publications

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Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved $L^{q}$ -estimates of second order derivatives uniformly in the angular and translational velocities,...

$L^{q}$ -approach to weak solutions of the Oseen flow around a rotating body

Stanislav Kračmar, Šárka Nečasová, Patrick Penel (2008)

Banach Center Publications

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We consider the time-periodic Oseen flow around a rotating body in ℝ³. We prove a priori estimates in $L^{q}$ -spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term -(ω ∧ x)·∇u + ω ∧ u in the equation of momentum where ω denotes the angular velocity. We prove the existence of generalized weak solutions...