Nonlinear Science and Complexity

1. Front Matter

   Pages I-XI

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2. Nonlinear Dynamics of Continuous and Discontinuous Dynamical Systems

   1. Front Matter

      Pages 1-1

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   2. On Synchronization and Its Complexity of Multiple Dynamical Systems

      • Albert C. J. Luo

      Pages 3-12

   3. Periodic and Chaotic Motions in a Gear-pair Transmission System with Impacts

      • Albert C. J. Luo, Dennis O’Connor

      Pages 13-24

   4. Analytical Prediction of Interrupted Cutting Periodic Motions in a Machine Tool

      • Brandon C. Gegg, Steve C. S. Suh, Albert C. J. Luo

      Pages 25-36

   5. Control of Hopf Bifurcation and Chaos as Applied to Multimachine System

      • Majdi M. Alomari, Benedykt S. Rodanski

      Pages 37-48

3. Lie Group Analysis and Applications in Nonlinear Sciences

   1. Front Matter

      Pages 49-49

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   2. Group-Invariant Solutions of Fractional Differential Equations

      • R. K. Gazizov, A. A. Kasatkin, S. Y. Lukashchuk

      Pages 51-59

   3. Type-II Hidden Symmetries for Some Nonlinear Partial Differential Equations

      • Maria Luz Gandarias

      Pages 61-66

   4. Nonclassical and Potential Symmetries for a Boussinesq Equation with Nonlinear Dispersion

      • M. S. Bruzón, M. L. Gandarias

      Pages 67-72

   5. Application of the Composite Variational Principle to Shallow Water Equations

      • Emrullah Yasar, Teoman Ozer

      Pages 73-78

   6. Conserved Forms of Second Order-Ordinary Differential Equations

      • C. Muriel, J. L. Romero

      Pages 79-84

   7. Analytical Investigation of a Two-Phase Model Describing a Three-Way-Catalytic Converter

      • J. Volkmann, N. Migranov

      Pages 85-92

4. Celestial Mechanics and Dynamical Astronomy: Methods and Applications

   1. Front Matter

      Pages 93-93

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   2. The Role of Invariant Manifolds in the Formation of Spiral Arms and Rings in Barred Galaxies

      • M. Romero-Gómez, E. Athanassoula, J. J. Masdemont, C. García-Gómez

      Pages 95-98

   3. Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three Body Problem

      • Michael Dellnitz, Kathrin Padberg, Robert Preis, Bianca Thiere

      Pages 99-105

   4. Low-Energy Transfers in the Earth–Moon System

      • Elisa Maria Alessi, Gerard Gómez, Josep J. Masdemont

      Pages 107-114

   5. Gravitational Potential of a Massive Disk. Dynamics Around an Annular Disk

      • E. Tresaco, A. Elipe, A. Riaguas

      Pages 115-121

   6. An Accounting Device for Biasymptotic Solutions: The Scattering Map in the Restricted Three Body Problem

      • Amadeu Delshams, Josep J. Masdemont, Pablo Roldán

      Pages 123-124

   7. Optimal Capture Trajectories Using Multiple Gravity Assists

      • Stefan Jerg, Oliver Junge, Shane D. Ross

      Pages 125-130

This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include • Chaotic Dynamics and Transport in Classic and Quantum Systems • Complexity and Nonlinearity in Molecular Dynamics and Nano-Science • Complexity and Fractals in Nonlinear Biological Physics and Social Systems • Lie Group Analysis and Applications in Nonlinear Science • Nonlinear Hydrodynamics and Turbulence • Bifurcation and Stability in Nonlinear Dynamic Systems • Nonlinear Oscillations and Control with Applications • Celestial Physics and Deep Space Exploration • Nonlinear Mechanics and Nonlinear Structural Dynamics • Non-smooth Systems and Hybrid Systems • Fractional dynamical systems

• NSC08
• complexity
• computational physics
• mathematics
• molecular dynamics
• nonlinear science
• structural dynamics

• Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Porto, Portugal

  J.A. Tenreiro Machado, Ramiro S. Barbosa, Manuel F. Silva, Lino B. Figueiredo

• Dept. of Mech. & Industr. Engineering, Southern Illinois Univ. Edwardsville, Edwardsville, USA

  Albert C.J. Luo

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