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=8356 A semi-invertible Oseledets Theorem with applications to transfer operator cocycles http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8356 A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems, Trudy Moskov. Mat. Obšč. 19 (1968), 179--210.] is concerned with the exponential growth rates of vectors under the action of a linear cocycle on $\mathbb{R}^d$. When the linear actions are invertible, the MET guarantees an almost-everywhere pointwise splitting of $\mathbb{R}^d$ into subspaces of distinct exponential growth rates (called Lyapunov exponents). When the linear actions are non-invertible, Oseledets' MET only yields the existence of a filtration of subspaces, the elements of which contain all vectors that grow no faster than exponential rates given by the Lyapunov exponents. The authors recently demonstrated [G. Froyland, S. Lloyd, and A. Quas, Coherent structures and exceptional spectrum for Perron--Frobenius cocycles, Ergodic Theory and Dynam. Systems 30 (2010), , 729--756.] that a splitting over $\mathbb{R}^d$ is guaranteed without the invertibility assumption on the linear actions. Motivated by applications of the MET to cocycles of (non-invertible) transfer operators arising from random dynamical systems, we demonstrate the existence of an Oseledets splitting for cocycles of quasi-compact non-invertible linear operators on Banach spaces. ]]> Gary Froyland, Simon Lloyd and Anthony Quas Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8357 On the non-homogeneous boundary value problem for Schrödinger equations http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8357 Corentin Audiard Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8358 Invariant measures for general induced maps and towers http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8358 Arno Berger and Roland Zweimüller Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8359 Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8359 Misha Bialy Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8360 Piecewise linear perturbations of a linear center http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8360 Claudio Buzzi, Claudio Pessoa and Joan Torregrosa Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8361 Liouville type theorems for poly-harmonic Navier problems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8361 1$.
    First we prove that (1) is equivalent to the following integral equation \begin{equation} u(x)=\int_{R^n_+}G(x,y,\alpha) u^p(y)dy,\,\,\,\,\, x\in\,R^n_+, \label{ie0} \end{equation} under some very mild growth condition, where $G(x, y,\alpha)$ is the Green's function associated with the same Navier boundary conditions on the half-space .
    Then by combining the method of moving planes in integral forms with a certain type of Kelvin transform, we obtain the non-existence of positive solutions for integral equation (2) in both subcritical and critical cases under only local integrability conditions. This remarkably weaken the global integrability assumptions on solutions in paper [3]. Our results on integral equation (2) are valid for all real values $\alpha$ between $0$ and $n$.
    Finally, we establish a Liouville type theorem for PDE (1), and this generalizes Guo and Liu's result [21] by significantly weaken the growth conditions on the solutions. ]]> Linfen Cao and Wenxiong Chen Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8362 Homeomorphisms group of normed vector space: Conjugacy problems and the Koopman operator http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8362 Mickaël D. Chekroun and Jean Roux Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8363 The CLT for rotated ergodic sums and related processes http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8363     Our aim is to extend this result and give a simple proof based on the Fejér-Lebesgue theorem. The results are expressed in the framework of processes generated by $K$-systems. We also consider the invariance principle for modified rotated sums. In a last section, we extend the method to $\mathbb{Z}^d$-dynamical systems. ]]> Guy Cohen and Jean-Pierre Conze Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8364 Bernoullicity of equilibrium measures on countable Markov shifts http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8364 Yair Daon Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8365 The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8365     The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane. ]]> Yuri N. Fedorov, Luis C. García-Naranjo and Joris Vankerschaver Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8366 Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8366 Sheng-Chen Fu and Je-Chiang Tsai Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8368 Heteroclinic limit cycles in competitive Kolmogorov systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8368 Zhanyuan Hou and Stephen Baigent Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8369 Resonant decomposition and the $I$-method for the two-dimensional Zakharov system http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8369 Nobu Kishimoto Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8370 The metric entropy of random dynamical systems in a Hilbert space: Characterization of invariant measures satisfying Pesin's entropy formula http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8370 Zhiming Li and Lin Shu Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8371 Simple skew category algebras associated with minimal partially defined dynamical systems http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8371 Patrik Nystedt and Johan Öinert Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8372 Endomorphisms of Sturmian systems and the discrete chair substitution tiling system http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8372 Jeanette Olli Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8373 Generalizations of analogs of theorems of Maizel and Pliss and their application in shadowing theory http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8373 Dmitry Todorov Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8374 Dynamics of spacing shifts http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8374 John Banks, Thi T. D. Nguyen, Piotr Oprocha, Brett Stanley and Belinda Trotta Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8375 Periodic points and periods for operators on hilbert space http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8375 P. Chiranjeevi, V. Kannan and Sharan Gopal Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8376 Ergodicity of group actions and spectral gap, applications to random walks and Markov shifts http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8376 Jean-Pierre Conze and Y. Guivarc'h Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8377 Spectral multiplicities for ergodic flows http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8377 Alexandre I. Danilenko and Mariusz Lemańczyk Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8378 Archimedean ice http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8378 Kari Eloranta Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8379 Regularity of topological cocycles of a class of non-isometric minimal homeomorphisms http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8379 Gernot Greschonig Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8380 Some advances on generic properties of the Oseledets splitting http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8380 Jana Rodriguez Hertz Sun, 1 Sep 2013 08:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8381 Dynamics on the infinite staircase http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=8381 W. Patrick Hooper, Pascal Hubert and Barak Weiss Sun, 1 Sep 2013 08:00:00 GMT