Difference Equations Discrete Dynamical Systems and Applications : ICDEA Barcelona Spain July 2012 These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems as well as the interplay between difference equations and dynamical systems. The conference was organized by the Department of Mathematics at the Universitat Autònoma de Barcelona (UAB) under the auspices of the International Society of Difference Equations (ISDE) and held in Barcelona (Catalonia Spain) in July 2012. Its purpose was to bring together experts and novices in these fields to discuss the latest developments. The book gathers contributions in the field of combinatorial and topological dynamics complex dynamics applications of difference equations to biology chaotic linear dynamics economic dynamics and control and asymptotic behavior and periodicity of difference equations. As such it is of interest to researchers and scientists engaged in the theory and applications of difference equations and discrete dynamical systems. Aija Anisimova: On the Second Order Rational Difference Equation $x_{n+1}=\\beta+\\frac{1}{x_n x_{n 1}}$ Dmitry Batenkov Gal Binyamini: Moment vanishing of piecewise solutions of linear ODEs Inese Bula: Periodic Solutions of the Second Order Quadratic Rational Difference Equation $x_{n+1}=\\frac{\\alpha}{(1+x_n)x_{n 1}}$ Antonio Cascales Francisco Balibrea: Li Yorke chaos in perturbed rational difference equations Robert L. Devaney Daniel Cuzzocreo: Simple Mandelpinski Necklaces for $z^2 + \\lambda z^2$ João P. Pais Almeida Miguel Ferreira Bruno Oliveira Alberto Pinto: R&D Dynamics with Asymmetric Efficiency Armengol Gasull Anna Cima Víctor Mañosa Francesc Mañosas: Different approaches to the global periodicity problem Marina Gonchenko Amadeu Delsham Sergey Gonchenko: On Bifurcations of Homoclinic Tangencies in Area Preserving Maps on Non Orientable Manifolds Goran Hognas: A compact invariant set for the Ricker competition model Goran Hognas: On a stochastic Ricker competition model José Martins Nilanjan Banik Alberto Pinto: A repeated strategy for dumping Marko Kostic: Hypercyclic and Topologically Mixing Properties of Certain Classes of Abstract Time Fractional Equations Jaume Llibre Juan Luis García Guirao: Periods of homeomorphisms on closed surfaces Joao Lopes Dias Gianluigi Del Magno Pedro Duarte Jose Pedro Gaivao Diogo Pinheiro: Polygonal billiards with a contractive reflection law: a review of some hyperbolic properties Hideaki Matsunaga: Asymptotic representation of solutions of linear autonomous difference equations Rafael Ortega: Translation arcs and stability in two dimensions Pedro J. Miana: Integrated exponential functions the Weyl fractional calculus and the Laplace transform Marc Rogalski Guy Bastien: A QRT system of two order one homographic difference equations: conjugation to rotations periods of periodic solutions sensitiveness to initial conditions Sanja Zivanovic Gonzalez Lev Kapitanski: Continuous Limit in Dynamics with Choice Guillermo Sienra Patricia Dominguez: Some Pinching deformations of the Fatou function Jakub Sotola: Answers to some problems on self similar sets and the open set condition Yosef Yomdin Dmitry Batenkov: Taylor Domination Difference Equations and Bautin Ideals Víctor Mañosa Guy Bastien Marc Rogalski: On the set of periods of the $2$ periodic Lyness Equation.