Recent Trends in Dynamical Systems, 2013 Proceedings of a Conference in Honor of Jürgen Scheurle Springer Proceedings in Mathematics & Statistics Series, Vol. 35

This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation - Geometric mechanics and control theory - Invariant manifolds, attractors and chaos - Fluid mechanics and elasticity - Perturbations and multiscale problems - Hamiltonian dynamics and KAM theory Researchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.

Part I Stability, Bifurcation & Perturbations.- 1 The Birth of Chaos.- 2 Periodic orbits close to grazing for an impact oscillator.- 3 Branches of Periodic Orbits in Reversible Systems.- 4 Canard explosion and position curves.- 5 Bifurcation for Non-smooth Dynamical Systems via Reduction Methods.- 6 Homoclinic flip bifurcations in conservative reversible systems.- 7 Local Lyapunov Functions for periodic and finite-time ODEs.- 8 Quasi-steady state: Searching for and utilizing small parameters.- 9 On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension.- 10 A Guided Sequential Monte Carlo Method for the Assimilation of Data Into Stochastic Dynamical Systems.- 11 Deterministic & Stochastic Dynamics of Chronic Myelogenous Leukaemia Stem Cells Subject to Hill-Function-Like Signaling.- Part II Hamiltonian Dynamics, Geometric Mechanics & Control Theory.- 12 Singular Solutions of Euler–Poincar´e Equations on Manifolds with Symmetry.- 13 On the destruction of resonant Lagrangean tori in Hamiltonian systems.- 14 Deformation of Geometry and Bifurcations of Vortex Rings.- 15 Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems.- 16 Boundary tracking and obstacle avoidance using gyroscopic control.- 17 Random Hill’s Equations, Random Walks, and Products of Random Matrices.- Part III Continuum Mechanics: Solids, Fluids and other Materials.- 18 The three dimensional globally modified Navier-Stokes equations: Recent developments.- 19 Simulation of Hard Contacts with Friction: An Iterative Projection Method.- 20 Dynamics of second grade fluids: the Lagrangian approach.- 21 Dissipative quantum mechanics using GENERIC.- 22 Modelling of thin martensitic films with nonpolynomial stored energies.- 23 Linear Stability of Steady Flows of Jeffreys Type Fluids.