Discrete and Continuous Dynamical Systems - Series A: latest papers
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Latest articles for selected journalhttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14178
Notes on a theorem of Katznelson and Ornstein
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1,$ where $\ell$ is Lebesgue measure.
We show that there exists a subset
of irrational numbers of unbounded type, such that for any element $\widehat{\rho}$
of this subset, the linear rotation $R_{\widehat{\rho}}$ and the shift
$f_{t}=f+t\mod 1,$ $t\in [0,1)$ with rotation number $\widehat{\rho},$ are
absolutely continuously conjugate. We also introduce a certain Zygmund-type condition
depending on a parameter $\gamma$, and prove that in the case $\gamma>\frac{1}{2}$ there exists a subset of
irrational numbers of unbounded type, such that every circle diffeomorphism satisfying the corresponding
Zygmund condition is absolutely continuously
conjugate to the linear rotation provided its rotation number belongs to the above set.
Moreover, in the case of $\gamma> 1,$ we show that the conjugacy is $C^{1}$-smooth.
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Habibulla Akhadkulov, Akhtam Dzhalilov and Konstantin KhaninFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14179
Polynomial approximation of self-similar measures and the spectrum of the transfer operator
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Christoph Bandt and Helena PeñaFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14180
Analytic dependence on parameters for Evans' approximated Weak KAM solutions
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Olga Bernardi and Matteo Dalla RivaFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14181
Asymptotic analysis of parabolic equations with stiff transport terms by a multi-scale approach
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Thomas Blanc, Mihai Bostan and Franck BoyerFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14182
Stability of stationary solutions to the compressible bipolar Euler--Poisson equations
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Hong Cai and Zhong TanFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14183
Spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media
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Feng Cao and Wenxian ShenFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14184
On a semilinear Timoshenko-Coleman-Gurtin system: Quasi-stability and attractors
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Baowei FengFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14185
Entropy of diffeomorphisms of line
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Also, we construct two examples:
1. there exists open subset $\mathcal{U}$ of Diff$^{\infty} (\mathbb{R})$ such that for any $f \in \mathcal{U}$, the entropy map with respect to strong $C^{\infty}$-topology, is not locally constant at $f$.
2. there exists $f \in$ Diff$^{\infty}(\mathbb{R})$ such that the entropy map with respect to strong $C^{\infty}$-topology, is neither lower semi-continuous nor upper semi-continuous at $f$.
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Baolin HeFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14186
Infimum of the metric entropy of volume preserving Anosov systems
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Huyi Hu, Miaohua Jiang and Yunping JiangFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14187
Qualitative analysis on positive steady-states for an autocatalytic reaction model in thermodynamics
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Yunfeng Jia, Yi Li and Jianhua WuFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14188
Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure
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Bum Ja Jin and Kyungkeun KangFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14189
Connected components of meanders: I. bi-rainbow meanders
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Closed meanders are planar configurations of
one or several disjoint closed Jordan curves intersecting
a given line transversely.
They arise as shooting curves of parabolic PDEs in one space dimension,
as trajectories of Cartesian billiards,
and as representations of elements of Temperley-Lieb algebras.
Given the configuration of intersections, for example as a permutation
or an arc collection, the number of Jordan curves is unknown. We address this question in the special case of bi-rainbow meanders,
which are given as non-branched families (rainbows) of nested arcs.
Easily obtainable results for small bi-rainbow meanders containing
at most four families in total (lower and upper rainbow families) suggest an expression of the number of curves by the
greatest common divisor (gcd) of polynomials in the sizes of the rainbow
families.We prove however, that this is not the case.
On the other hand, we provide a complexity analysis of
nose-retraction algorithms.
They determine the number of connected components of arbitrary
bi-rainbow meanders in logarithmic time.
In fact, the nose-retraction algorithms resemble the Euclidean algorithm.
Looking for a closed formula of the number of connected components,
the nose-retraction algorithm is as good as a gcd-formula and therefore
as good as we can possibly expect.
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Anna Karnauhova and Stefan LiebscherFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14190
General decay of solutions of a Bresse system with viscoelastic boundary conditions
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Ammar Khemmoudj and Taklit HamadoucheFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14191
Strichartz estimates for Schrödinger equations in weighted $L^2$ spaces and their applications
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1$
with radial data $f,F$ with respect to the spatial variable $x$,
whenever the weight is in a Morrey-Campanato type class.
This is done by making use of a useful property of maximal functions of the weights
together with frequency-localized estimates which follow from using
bilinear interpolation and some estimates of Bessel functions.
As consequences, we give an affirmative answer to a question posed in [1]
concerning weighted homogeneous Strichartz estimates,
and improve previously known Morawetz estimates.
We also apply the weighted $L^2$ estimates to the well-posedness theory for the
Schrödinger equations with time-dependent potentials in the class.
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Youngwoo Koh and Ihyeok SeoFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14192
Global strong solution for the incompressible flow of liquid
crystals with vacuum in dimension two
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Xiaoli LiFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14193
Hyperbolic sets that are not contained in a locally maximal one
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Question.Let $\Lambda$ be a hyperbolic set, and let $V$ be an open neighborhood of
$\Lambda$. Does there exist a locally maximal hyperbolic set $\widetilde{\Lambda}$
such that $\Lambda \subset \widetilde{\Lambda} \subset V $?

We show that such examples are present in linear Anosov diffeomorophisms of $\mathbb{T}^3$,
and are therefore robust.
Also we construct new examples of sets that are not contained in any locally maximal hyperbolic set.
The examples known until now were constructed by Crovisier in [7] and by Fisher in [9], and these were either in dimension
equal or bigger than 4 or they were not transitive.
We give a transitive and robust example in
$\mathbb{T}^3$. And show that such examples cannot be build in dimension 2.
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Adriana da LuzFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14194
On averaged tracing of periodic average pseudo orbits
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Piotr Oprocha and Xinxing WuFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14195
Fiber bunching and cohomology for Banach cocycles over hyperbolic systems
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Victoria SadovskayaFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14196
Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials
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Xianhua Tang and Sitong ChenFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14197
Almost sure existence of global weak solutions to the 3D incompressible Navier-Stokes equation
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0$. This improves the recent result of Nahmod, Pavlovié and Staffilani on (SIMA) in which $\alpha$ is restricted to $0< \alpha <\frac{1}{4}$.
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Jingrui Wang and Keyan WangFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14198
Boundedness in logistic Keller--Segel models with nonlinear diffusion and sensitivity functions
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0, \\
v_t=\Delta v-v+u,&x \in \Omega,t>0, \\
\frac{\partial u}{\partial \nu}=\frac{\partial v}{\partial \nu}=0,&x\in\partial \Omega,t>0
\end{array}
\right.\]
over a multi--dimensional bounded domain $\Omega \subset \mathbb R^N$, $N\geq2$. Here $D(u)$ and $S(u)$ are smooth functions satisfying: $D(0)>0$, $D(u)\geq K_1u^{m_1}$ and $S(u)\leq K_2u^{m_2}$, $\forall u\geq0$, for some constants $K_i\in\mathbb R^+$, $m_i\in\mathbb R$, $i=1,2$. It is proved that, when the parameter pair $(m_1,m_2)$ lies in some specific regions, the system admits global classical solutions and they are uniformly bounded in time. We cover and extend [22,28], in particular when $N\geq3$ and $\gamma\geq1$, and [3,29] when $m_1>\gamma-\frac{2}{N}$ if $\gamma\in(0,1)$ or $m_1>\gamma-\frac{4}{N+2}$ if $\gamma\in[1,\infty)$. Moreover, according to our results, the index $\frac{2}{N}$ is, in contrast to the model without cellular growth, no longer critical to the global existence or collapse of this system.
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Qi Wang, Jingyue Yang and Feng YuFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14199
Global solution for the $3D$ quadratic Schrödinger equation of $Q(u,\bar{u}$) type
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In this paper, we show that, as long as there are ``$\epsilon$'' derivatives inside the quadratic term $Q (u, \bar{u})$, there exists a global solution for small initial data. As a byproduct, we also give a simple proof for the almost global existence of the small data solution of $(∂_t -i \Delta)u = |u|^2 = u\bar{u}$, which was first proved by Ginibre-Hayashi [3]. Instead of using vector fields, we consider this problem purely in Fourier space.
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Xuecheng WangFri, 1 Sep 2017 08:00:00 GMThttp://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14200
A characterization of Sierpiński carpet rational maps
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Yan Gao, Jinsong Zeng and Suo ZhaoFri, 1 Sep 2017 08:00:00 GMT