Galaxies and chaos : [Workshop "Galaxies and Chaos, Theory and Observations" held in Athens in September 16-19, 2002 ; selected presentations

Galaxies And Chaos Examines The Application Of Tools Developed For Nonlinear Dynamical Systems To Galactic Dynamics And Galaxy Formation, As Well As To Related Issues In Celestial Mechanics. The Contributions Collected In This Volume Have Emerged From Selected Presentations At A Workshop On This Topic And Key Chapters Have Been Suitably Expanded In Order To Be Accessible To Nonspecialist Researchers And Postgraduate Students Wishing To Enter This Exciting Field Of Research. Order And Chaos -- Orbit Theory -- Observations -- Formation And Evolution Of Galaxies -- Solar System Dynamics. G. Contopoulos, N. Voglis (eds.). Includes Bibliographical References. front-matter Chapter 1 1 Introduction 2 Celestial Mechanics 3 Classification of Chaotic Systems 4 Galactic Dynamics 5 Chaotic Orbits in Galaxies 6 Diffusion of Galactic Orbits 7 Escapes 8 Dissipative Systems 9 Chaos in Relativity and Cosmology 10 Chaos in Stellar Pulsations 11 Chaos in Solar Activity References Chapter 2 1 Introduction 2 Exact Special Cases 3 Drift Trajectories – Ergos Curves 4 The Gyration Adiabatic Invariant 5 Is the Saddle-Point Switch Chaotic? References Chapter 3 1 Introduction 2 Planck ’s Law,Its Interpretation by Einstein, and the Points of View of Boltzmann and of Nernst 3 The Fermi–Pasta–Ulam Problem 4 The Landau–Teller Model of Molecular Collisions 5 Conclusions References Chapter 4 1 Introduction 2 Solitons of Non-interacting Particles Moving in a Given Potential 3 Linear Epicyclic Waves in Galactic Models 5 Non-linear Epicyclic Motion near the Inner Lindblad Resonance 6 A Sine-Gordon Equation 7 Analytic Solutions 8 A Numerical Application and Comparison with the Analytic Results 9 Summary and Discussion Acknowledgments References Chapter 5 1 The History of Energy Localization 1.1 The Discovery of Discrete Breathers 2 The Connection with Homoclinic Dynamics 2.1 How to Construct Homoclinic Orbits 3 A New Approach Is Introduced 3.1 Stability and Existence of Discrete Breathers Using Control Acknowledgements References Chapter 6 1 Introduction 2 The Epicyclic Solution for Any Number of Bars 2.1 Closed Periodic Orbits in a Single Bar 2.2 Loops in Double Bars 3 Full Nonlinear Solution for Loops in Nested Bars 4 Conclusions Acknowledgments References Chapter 7 1 Introduction 2 The Jeans Equations for Separable Models 3 The Two-Dimensional Case 4 The General Case 5 Discussion and Conclusions References Chapter 8 1 Introduction 2 Basic Equations 3 Ultra Harmonic Resonances 3.1 The Resonant Case of omega_0 pprox 2 3.2 The Resonant Case of omega_0 pprox 3 4 Interpretation of the Results References Chapter 9 1 Introduction 2 Method to Distinguish Regular and Chaotic Orbits 2.1 Specific Finite Time Lyapunov Characteristic Number 2.2 Common Unit Finite Time LCN 2.3 Alignment Index 3 Results 4 Conclusions References Chapter 10 1 Introduction 2 The Low Frequency Domain and Underlying Dynamics 3 Estimation of the Low Frequency Power and Asymptotic Characteristics 4 Numerical Results and Conclusions Acknowledgements References Chapter 11 1 Introduction 2 Models 2.1 Kuzmin ’s Disk 2.2 Kuzmin-Like Potentials 2.3 The Logarithmic Kuzmin-Like Potentials 3 Dynamics 4 Orbits 4.1 Orbits in Kuzmin ’s Disk 4.2 Orbits in Kuzmin-Like Potentials 5 Thickened Disks 6 Discussion and Conclusions 6.1 Related Work 6.2 Conclusions Acknowledgements References Chapter 12 1 Introduction 2 Transient Chaos and Collisionless Relaxation 2.1 Transient Chaos Induced by Parametric Resonance 2.2 Chaotic Phase Mixing and Collisionless Relaxation 3 The Role of Discreteness E.ects 3.1 Microchaos and Macrochaos 3.2 Modeling Discreteness E.ects as Friction and Noise 4 Experimental Tests of Galactic Dynamics 4.1 Similarities Between Galaxies and Nonneutral Plasmas 4.2 Testing Galaxy Evolution with Charged Particle Beams 5 Conclusions References Chapter 13 1 Experimental Details 1.1 Generalities 1.2 Loader 1.3 Integrator 2 Results from Experiments 2.1 Nature of MP Motions 2.2 MP Energies and Effective Masses 2.3 The Run with MP =100K 2.4 External Harmonic Potential 2.5 Other Features 3 Discussion 3.1 The Relation Between Actual and Effective MP Masses 3.2 Theoretical Approaches References Chapter 14 1 Introduction 2 Structure of Bright Elliptical Galaxies 3 Mechanisms of Dynamical Evolution 4 General Trends from Thermodynamical Arguments 5 Conclusions Acknowledgements References Chapter 15 1 Introduction 2 Environment 3 Regions of Chaos 4 Chaos in the Galaxy 5 Tracers of Chaos in External Galaxies 6 Observational Considerations 7 Feasibility of Observing Chaos 8 Conclusions References Chapter 16 1 Introduction 2 Methods to Determine the Pattern Speed 3 The Case of NGC 1365 References Chapter 17 1 Introduction 2 Restored Velocity Field of the Grand Design Spiral Galaxy NGC 3631 3 The Calculation of the Lyapunov Characteristic Numbers 4 Spectrum of the Stretching Numbers 5 Conclusions Acknowledgments References Chapter 18 1 Introduction 2 The Simplest Theory 2.1 Qualitative Considerations 2.2 Model Examples 3 Example of QTS in the Galaxy NGC 3631 4 Conclusions Acknowledgments References Chapter 19 1 Introduction 2 General Considerations 2.1 Scope 2.2 Spiral Galaxies 2.3 The Gravitational Potential 3 Spherical Potentials 4 Axisymmetric Potentials 4.1 Two-Integral Dynamical Models 4.2 Three-Integral Dynamical Models 5 What Can We Learn from Distribution Functions? 5.1 Disentangle Photometric and Kinematic Information 5.2 Additional Classification Parameter 5.3 Counterrotation in NGC 7097 6 Continuous Improving on Modelling Techniques 6.1 Spectra as Source of Information 6.2 Construction of a Third Integral 7 Some Concerns Before Modelling Takes of 7.1 Influence of Dust 7.2 Error Bars on Data 8 Conclusions References Chapter 20 1 Introduction 2 Observations and Data Reduction 3 Results 4 Discussion 5 Conclusion References Chapter 21 1 Introduction 2 No Cuspy Halos in LSB Galaxies 2.1 Expectations vs.Observations 2.2 Reply to Some Criticism 2.3 Further Observations and Modelling OF Possible Errors 3 Spirals 3.1 Importance of Good Data in the Inner Parts 3.2 Importance of Disk Self-gravity 3.3 Lensing Data 4 Conclusion Acknowledgements References Chapter 22 1 The SAURON Project 2 Dynamical Models 3 Axisymmetric Models for M32 4 The Triaxial Galaxy NGC 4365 5 Concluding Remarks References Chapter 23 1 Review 2 Interactions,Mergers and Evolution 3 Surface Photometry 4 Deviations from Perfect Ellipticity 5 Isophotal Twist 6 The Holmberg Effect 7 Summary References Chapter 24 1 Introduction 2 The Spline Histogram Algorithm 3 Simulated Data Analysis 4 Galaxy Cluster Data Analysis 5 Concluding Remarks Acknowledgments References Chapter 25 1 Introduction 2 Mass Estimate for the Inner Cusp 2.1 Stellar Density 2.2 The Enclosed Mass 3 Estimate of the Line of Sight Positions of 13 Helium Stars Acknowledgements References Chapter 26 1 Introduction 2 Angular Momentum Exchange and Bar Evolution 3 The Effect of the Halo on Bar Evolution 4 Bar Slow-Down 5 Resonances 6 What Determines the Strength of Bars and Their Slow-Down Rate? 7 Trends and Correlations 8 Comparing the Morphology of N -Body and of Real Bars 9 Summary Acknowledgments References Chapter 27 1 Introduction 2 The Merger Models 3 Photometric and Kinematical Properties of the Remnants 3.1 Isophotal Shape 3.2 Kinematics 4 Conclusions Acknowledgement References Chapter 28 1 Introduction 2 N -Body Simulations 3 Results of Simulations 3.1 Modified Stability Criterion 3.2 Chaotic Velocity Diffusion References Chapter 29 1 Introduction 2 The Model 3 Results and Discussion 3.1 The Halo Field Stars of Our and Some Other Galaxies 3.2 A Globular Cluster System of Our and Some Other Galaxies 4 Conclusions References Chapter 30 1 Introduction 2 Two Shells Around SBH 3 Numerical Solution 4 Chaos in the Shell Motion Acknowledgement References Chapter 31 Introduction 1 Basic Features of the Direct Scenario 2 Counterrotation from Clumpy Cosmological Initial Conditions 3 Counterrotation from Merging with a Satellite Galaxy 4 Comparison of the Results and Discussion Acknowledgements References Chapter 32 1 Introduction 2 Prediction by the Density Wave Theory 3 Models and Method 4 Results 5 Discussion and Conclusions References Chapter 33 1 Introduction 2 The Physical Background 3 Galaxy and Cluster Models 4 Preliminary Results and Conclusions References Chapter 34 1 Introduction 2 The n-Body Solar System 2.1 Outline of the Classical Perturbation Method 2.2 High Order Resonances,Secular Resonances and the Fundamental Frequencies 3 Dynamics of Comets and Asteroids 4 The Planets 4.1 Numerical Solutions 4.2 Determination of the Fundamental Frequencies 4.3 Mercury as Perturber of the Inner System 4.4 The Obliquity of Planets 5 Conclusions 6 Epilog Acknowledgements References Chapter 35 1 Introduction 2 Families of Periodic Orbits 2.1 Periodic Orbits in the Rotating Frame 2.2 Periodic Orbits of the Planetary Type 2.3 Families of Periodic Orbits at the 2/1 Resonance 3 The Different Types of 2/1 Resonant Periodic Orbits 3.1 Stable Orbits of the Families I and IV 3.2 A Stable and an Unstable Orbit of the Family II 3.3 Two Orbits of the Unstable Family IV 3.4 The Periodic Orbits in the Synodic Frame 4 Perturbed Orbits Close to Stable and Unstable Periodic Orbits 4.1 Perturbed Orbits Close to the Orbit 1 and the Orbit 4 4.2 Perturbed Orbits Close to the Orbit 2 and the Orbit 3 4.3 Perturbed Orbits Close to the Orbit 5 5 Discussion Acknowledgements References Chapter 36 1 Introduction 2 The Way Things Might Have Happened 2.1 Ordered Trajectories 2.2 Chaotic Trajectories 3 The Way Things Really Happened References