Recent Trends in Dynamical Systems

Part I. Stability, Bifurcation and Perturbations

1. The Birth of Chaos
John Guckenheimer

2. Periodic Orbits Close to Grazing for an Impact Oscillator
D. R. J. Chillingworth, A. B. Nordmark

3. Branches of Periodic Orbits in Reversible Systems
André Vanderbauwhede

4. Canard Explosion and Position Curves
Freddy Dumortier

5. Bifurcation for Non-smooth Dynamical Systems via Reduction Methods
T. Küpper, H. A. Hosham, D. Weiss

6. Homoclinic Flip Bifurcations in Conservative Reversible Systems
Björn Sandstede

7. Local Lyapunov Functions for Periodic and Finite-Time ODEs
Peter Giesl, Sigurdur Hafstein

8. Quasi-Steady State: Searching for and Utilizing Small Parameters
Alexandra Goeke, Sebastian Walcher

9. On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension
Messoud Efendiev, Anna Zhigun

10. A Guided Sequential Monte Carlo Method for the Assimilation of Data into Stochastic Dynamical Systems
Sebastian Reich

11. Deterministic and Stochastic Dynamics of Chronic Myelogenous Leukaemia Stem Cells Subject to Hill-Function-Like Signaling
Tor Flå, Florian Rupp, Clemens Woywod

Part II. Hamiltonian Dynamics, Geometric Mechanics and Control Theory

12. Singular Solutions of Euler–Poincaré Equations on Manifolds with Symmetry
D. D. Holm, J. Munn, S. N. Stechmann

13. On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems
Henk W. Broer, Heinz Hanßmann, Jiangong You

14. Deformation of Geometry and Bifurcations of Vortex Rings
James Montaldi, Tadashi Tokieda

15. Gradient Flows in the Normal and Kähler Metrics and Triple Bracket Generated Metriplectic Systems
Anthony M. Bloch, Philip J. Morrison, Tudor S. Ratiu

16. Boundary Tracking and Obstacle Avoidance Using Gyroscopic Control
Fumin Zhang, Eric W. Justh, P. S. Krishnaprasad

17. Random Hill’s Equations, Random Walks, and Products of Random Matrices
Fred C. Adams, Anthony M. Bloch, Jeffrey C. Lagarias

Part III. Continuum Mechanics: Solids, Fluids and Other Materials

18. The Three-Dimensional Globally Modified Navier–Stokes Equations: Recent Developments
T. Caraballo, P. E. Kloeden

19. Simulation of Hard Contacts with Friction: An Iterative Projection Method
Christoph Glocker

20. Dynamics of Second Grade Fluids: The Lagrangian Approach
M. Paicu, G. Raugel

21. Dissipative Quantum Mechanics Using GENERIC
Alexander Mielke

22. Modelling of Thin Martensitic Films with Nonpolynomial Stored Energies
Martin Kružík, Johannes Zimmer

23. Linear Stability of Steady Flows of Jeffreys Type Fluids
Michael Renardy

Keywords: Mathematics, Dynamical Systems and Ergodic Theory, Mathematical Physics