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Recent Trends in Dynamical Systems

Proceedings of a Conference in Honor of Jürgen Scheurle

  • Conference proceedings
  • © 2013

Overview

Editors:
  1. Andreas Johann

    1. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

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  2. Hans-Peter Kruse

    1. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

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  3. Florian Rupp

    1. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

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  4. Stephan Schmitz

    1. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

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Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 35)

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Table of contents (23 papers)

  1. Front Matter

    Pages i-xxv
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  2. Stability, Bifurcation and Perturbations

    1. Front Matter

      Pages 1-1
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    2. The Birth of Chaos

      • John Guckenheimer
      Pages 3-24

    3. Periodic Orbits Close to Grazing for an Impact Oscillator

      • D. R. J. Chillingworth, A. B. Nordmark
      Pages 25-37

    4. Branches of Periodic Orbits in Reversible Systems

      • André Vanderbauwhede
      Pages 39-49

    5. Canard Explosion and Position Curves

      • Freddy Dumortier
      Pages 51-78

    6. Bifurcation for Non-smooth Dynamical Systems via Reduction Methods

      • T. Küpper, H. A. Hosham, D. Weiss
      Pages 79-105

    7. Homoclinic Flip Bifurcations in Conservative Reversible Systems

      • Björn Sandstede
      Pages 107-123

    8. Local Lyapunov Functions for Periodic and Finite-Time ODEs

      • Peter Giesl, Sigurdur Hafstein
      Pages 125-152

    9. Quasi-Steady State: Searching for and Utilizing Small Parameters

      • Alexandra Goeke, Sebastian Walcher
      Pages 153-178

    10. On a Global Uniform Pullback Attractor of a Class of PDEs with Degenerate Diffusion and Chemotaxis in One Dimension

      • Messoud Efendiev, Anna Zhigun
      Pages 179-203

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

      • Sebastian Reich
      Pages 205-220

    12. Deterministic and Stochastic Dynamics of Chronic Myelogenous Leukaemia Stem Cells Subject to Hill-Function-Like Signaling

      • Tor Flå, Florian Rupp, Clemens Woywod
      Pages 221-263

  3. Hamiltonian Dynamics, Geometric Mechanics and Control Theory

    1. Front Matter

      Pages 265-265
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    2. Singular Solutions of Euler–Poincaré Equations on Manifolds with Symmetry

      • D. D. Holm, J. Munn, S. N. Stechmann
      Pages 267-316

    3. On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems

      • Henk W. Broer, Heinz Hanßmann, Jiangong You
      Pages 317-333

    4. Deformation of Geometry and Bifurcations of Vortex Rings

      • James Montaldi, Tadashi Tokieda
      Pages 335-370

    5. Gradient Flows in the Normal and Kähler Metrics and Triple Bracket Generated Metriplectic Systems

      • Anthony M. Bloch, Philip J. Morrison, Tudor S. Ratiu
      Pages 371-415

    6. Boundary Tracking and Obstacle Avoidance Using Gyroscopic Control

      • Fumin Zhang, Eric W. Justh, P. S. Krishnaprasad
      Pages 417-446

    7. Random Hill’s Equations, Random Walks, and Products of Random Matrices

      • Fred C. Adams, Anthony M. Bloch, Jeffrey C. Lagarias
      Pages 447-470
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Keywords

About this book

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.

Editors and Affiliations

  • Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

    Andreas Johann, Hans-Peter Kruse, Florian Rupp, Stephan Schmitz

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