This volume holds a collection of articles based on the talks presented at IEA 2007 in Lisbon, Portugal.The volume encompasses current topics on stability and bifurcation, chaos, mathematical biology, iteration theory, nonautonomous systems, and stochastic dynamical systems.Contents:Combinatorics of Newton Maps on Quintic Equations (F Balibrea)Hyperbolic Dynamics in Nash Maps (R A Becker et al.)Attractive Cycles of an Artificial Neural Network (S S Cheng & X-L Liu)Hyperbolic and Minimal Sets (A A Pinto)Difference Equations with Continuous Time: Theory and Applications (E Y Romanenko & A N Sharkovsky)Lyapunov-Schmidt: A Discrete Revision (A Vanderbauwhede)Pinto's Golden Tilings (J P Almeida)Non-Exponential Stability and Decay Rates in Nonlinear Stochastic Homogeneous Difference Equations (J A D Appleby et al.)Interval Maps and Cellular Automata (L Bandeira et al.)Difference Equations on Matrix Algebras (A N Baptista et al.)and other papersReadership: Academics, graduate students and researchers in mathematics, physics and engineering.