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=14028 Gevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed points http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14028 parabolic direction of fixed points of analytic maps, that is, a direction associated with an eigenvalue equal to $1$. We show that, under general hypotheses, these invariant manifolds are Gevrey with type related to some explicit constants. We provide examples of the optimality of our results as well as some applications to celestial mechanics, namely, the Sitnikov problem and the restricted planar three body problem. ]]> Inmaculada Baldomá, Ernest Fontich and Pau Martín Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14029 Existence of minimal flows on nonorientable surfaces http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14029 José Ginés Espín Buendía, Daniel Peralta-Salas and Gabriel Soler López Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14030 Positive ground state solutions for a quasilinear elliptic equation with critical exponent http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14030 Yinbin Deng and Wentao Huang Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14031 Separated nets arising from certain higher rank $\mathbb R^k$ actions on homogeneous spaces http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14031 Changguang Dong Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14032 On nonlocal symmetries generated by recursion operators: Second-order evolution equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14032 M. Euler, N. Euler and M. C. Nucci Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14033 The geometric discretisation of the Suslov problem: A case study of consistency for nonholonomic integrators http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14033     Cortés and Martínez [4] claim that choosing $L_d$ and $D_d$ in a consistent manner with respect to a finite difference map is necessary to guarantee an approximation of the continuous flow within a desired order of accuracy. Although this statement is given without proof, similar versions of it have appeared recently in the literature.
    We evaluate the importance of the consistency condition by comparing the performance of two different geometric integrators for the nonholonomic Suslov problem, only one of which corresponds to a consistent choice of $L_d$ and $D_d$. We prove that both integrators produce approximations of the same order, and, moreover, that the non-consistent discretisation outperforms the other in numerical experiments and in terms of energy preservation. Our results indicate that the consistency of a discretisation might not be the most relevant feature to consider in the construction of nonholonomic geometric integrators. ]]>
Luis C. García-Naranjo and Fernando Jiménez Tue, 1 Aug 2017 20:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14034 Analysis of a Cahn--Hilliard system with non-zero Dirichlet conditions modeling tumor growth with chemotaxis http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14034 Harald Garcke and Kei Fong Lam Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14035 Orbital stability and uniqueness of the ground state for the non-linear Schrödinger equation in dimension one http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14035 Daniele Garrisi and Vladimir Georgiev Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14036 On coupled Dirac systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14036 1$ satisfy $$ \frac{1}{p+1}+\frac{1}{q+1}>\frac{n-1}{n}. $$ In this case we obtain infinitely many solutions of the coupled Dirac system by using a generalized fountain theorem. ]]> Wenmin Gong and Guangcun Lu Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14037 Statistical and deterministic dynamics of maps with memory http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14037 Paweł Góra, Abraham Boyarsky, Zhenyang Li and Harald Proppe Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14038 Livšic theorem for banach rings http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14038 Genady Ya. Grabarnik and Misha Guysinsky Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14039 Exact azimuthal internal waves with an underlying current http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14039 Hung-Chu Hsu Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14040 Existence of heterodimensional cycles near Shilnikov loops in systems with a $\mathbb{Z}_2$ symmetry http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14040 Dongchen Li and Dmitry V. Turaev Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14041 On the uniqueness of solution to generalized Chaplygin gas http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14041 Marko Nedeljkov and Sanja Ružičić Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14042 Normalization in Banach scale Lie algebras via mould calculus and applications http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14042 Thierry Paul and David Sauzin Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14043 Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14043 0,\ \ v(x)>0,\ \ & x\in \Omega,\\ u(x)=v(x)=0,\ \ & x\in\partial\Omega, \end{array}\right. \end{eqnarray*} where $-\infty< p <1$, $-1 < s$, and $q, r, d_1, d_2$ are positive constants, $a_1,\,a_2$ are nonnegative constants, $\rho_1,\,\rho_2$ are smooth nonnegative functions and $\Omega\subset \mathbb{R}^d\,(d\geq1)$ is a bounded smooth domain. New sufficient conditions, some of which are necessary, on the existence of classical solutions are established. A uniqueness result of solutions in any space dimension is also derived. Previous results are substantially improved; moreover, a much simpler mathematical approach with potential application in other problems is developed. ]]> Rui Peng, Xianfa Song and Lei Wei Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14044 Non-autonomous stochastic evolution equations in Banach spaces of martingale type 2: Strict solutions and maximal regularity http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14044 Tôn Việt Tạ Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14045 Measurable sensitivity via Furstenberg families http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14045     Let $\mathcal{F}_t$ (resp. $\mathcal{F}_{ip}$) be the families consisting of thick sets (resp. IP-sets). The following Auslander-Yorke's type dichotomy theorems are obtained: (1) a minimal system is either $\mathcal{F}_{t}$-sensitive for $\mu$ or an almost one-to-one extension of its maximal equicontinous factor. (2) a minimal system is either block $\mathcal{F}_{t}$-sensitive for $\mu$ or a proximal extension of its maximal equicontinous factor. (3) a minimal system is either block $\mathcal{F}_{ip}$-sensitive for $\mu$ or an almost one-to-one extension of its $\infty$-step nilfactor.
    We also introduce the notion of topological $l$-sensitivity, and construct a minimal system which is $l$-sensitive but not $(l+1)$-sensitive for $l\in\mathbb{N}$. ]]>
Tao Yu Tue, 1 Aug 2017 20:00:00 GMT
http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14046 Ground state solutions for Hamiltonian elliptic system with inverse square potential http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14046 0$ and $\mu=0$. Finally, we also give the convergence property of ground state solutions as $\mu\to0^+$. ]]> Jian Zhang, Wen Zhang and Xianhua Tang Tue, 1 Aug 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14047 Corrigendum to "Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology" http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=14047 Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez and Alberto Verjovsky Tue, 1 Aug 2017 20:00:00 GMT