Recent Trends in Dynamical Systems: Proceedings of a Conference in Honor of Jürgen Scheurle

ISBN-13: 9783034804509 / Angielski / Twarda / 2013 / 616 str.

Andreas Johann; Hans-Peter Kruse; Florian Rupp

Opis

This book presents the proceedings of a conference on dynamical systems held in honor of Jurgen 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.

Spis treści

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.

Blurb

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.

Contributors:

Fred C. Adams
Henk W. Broer
Anthony M. Bloch
Tomas Caraballo
David R.J. Chillingworth
Freddy Dumortier
Messoud Efendiev
Tor Flå
Peter A. Giesl
Christoph Glocker
Alexandra Goeke
John Guckenheimer
Sigurdur Hafstein
Heinz Hanßmann
Darryl D. Holm
Hany  A. Hosham
Eric W. Justh
Peter E. Kloeden
P. S. Krishnaprasad
Martin Kružík
Tassilo Küpper
Alexander Mielke
James Montaldi
Philip J. Morrison
Jonathan Munn
Arne B. Nordmark
Marius Paicu
Tudor S. Ratiu
Geneviève Raugel
Sebastian Reich
Michael Renardy
Florian H.-H. Rupp
Björn Sandstede
Samuel N. Stechmann
Tadashi Tokieda
André Vanderbauwhede
Sebastian Walcher
Daniel Weiss
Clemens Woywod
Jiangong You
Fumin Zhang
Anna Zhigun
Johannes Zimmer