Discrete and Continuous Dynamical Systems - Series A: latest papers http://www.aimsciences.org/test_aims/journals/rss.jsp?journalID=1 Latest articles for selected journal http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14178 Notes on a theorem of Katznelson and Ornstein http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14178 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. ]]> Habibulla Akhadkulov, Akhtam Dzhalilov and Konstantin Khanin Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14179 Polynomial approximation of self-similar measures and the spectrum of the transfer operator http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14179 Christoph Bandt and Helena Peña Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14180 Analytic dependence on parameters for Evans' approximated Weak KAM solutions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14180 Olga Bernardi and Matteo Dalla Riva Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14181 Asymptotic analysis of parabolic equations with stiff transport terms by a multi-scale approach http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14181 Thomas Blanc, Mihai Bostan and Franck Boyer Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14182 Stability of stationary solutions to the compressible bipolar Euler--Poisson equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14182 Hong Cai and Zhong Tan Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14183 Spreading speeds and transition fronts of lattice KPP equations in time heterogeneous media http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14183 Feng Cao and Wenxian Shen Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14184 On a semilinear Timoshenko-Coleman-Gurtin system: Quasi-stability and attractors http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14184 Baowei Feng Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14185 Entropy of diffeomorphisms of line http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14185     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 $f$. ]]>
Baolin He Fri, 1 Sep 2017 08:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14186 Infimum of the metric entropy of volume preserving Anosov systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14186 Huyi Hu, Miaohua Jiang and Yunping Jiang Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14187 Qualitative analysis on positive steady-states for an autocatalytic reaction model in thermodynamics http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14187 Yunfeng Jia, Yi Li and Jianhua Wu Fri, 1 Sep 2017 08:00:00 GMT http://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 http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14188 Bum Ja Jin and Kyungkeun Kang Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14189 Connected components of meanders: I. bi-rainbow meanders http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14189 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. ]]>
Anna Karnauhova and Stefan Liebscher Fri, 1 Sep 2017 08:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14190 General decay of solutions of a Bresse system with viscoelastic boundary conditions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14190 Ammar Khemmoudj and Taklit Hamadouche Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14191 Strichartz estimates for Schrödinger equations in weighted $L^2$ spaces and their applications http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14191 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. ]]> Youngwoo Koh and Ihyeok Seo Fri, 1 Sep 2017 08:00:00 GMT http://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 http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14192 Xiaoli Li Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14193 Hyperbolic sets that are not contained in a locally maximal one http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14193
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. ]]>
Adriana da Luz Fri, 1 Sep 2017 08:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14194 On averaged tracing of periodic average pseudo orbits http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14194 Piotr Oprocha and Xinxing Wu Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14195 Fiber bunching and cohomology for Banach cocycles over hyperbolic systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14195 Victoria Sadovskaya Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14196 Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with general potentials http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14196 Xianhua Tang and Sitong Chen Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14197 Almost sure existence of global weak solutions to the 3D incompressible Navier-Stokes equation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14197 0$. This improves the recent result of Nahmod, Pavlovié and Staffilani on (SIMA) in which $\alpha$ is restricted to $0< \alpha <\frac{1}{4}$. ]]> Jingrui Wang and Keyan Wang Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14198 Boundedness in logistic Keller--Segel models with nonlinear diffusion and sensitivity functions http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14198 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. ]]> Qi Wang, Jingyue Yang and Feng Yu Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14199 Global solution for the $3D$ quadratic Schrödinger equation of $Q(u,\bar{u}$) type http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14199     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. ]]> Xuecheng Wang Fri, 1 Sep 2017 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14200 A characterization of Sierpiński carpet rational maps http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14200 Yan Gao, Jinsong Zeng and Suo Zhao Fri, 1 Sep 2017 08:00:00 GMT