Chaos and Complexity in Astrophysics
The discipline of nonlinear dynamics has developed explosively in all areas of physics over the last two decades. This comprehensive primer summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Oded Regev demonstrates the possible application of ideas including strange attractors, Poincaré sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems.
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Introduction to Part I
Mathematical properties of dynamical systems
Properties of chaotic dynamics
Analysis of time series
Regular and irregular motion in Hamiltonian systems
Extended systems instabilities and patterns
Introduction to Part II
Irregularly variable astronomical point sources
Complex spatial patterns in astrophysics
Topics in astrophysical fluid dynamics
accretion accretion disc analysis analytical approach astrophysical attractor basic bifurcation boundary conditions calculations chaos chaotic behaviour Chapter complex consider constant convection corresponding curve defects defined depends derived detail dimensional discrete discussion dissipative dynamical system eigenvalues energy equilibrium evolution example finite fixed point flow fluid dynamics Fourier fractal dimension frequency function galaxy gravitational Hamiltonian systems homoclinic Hopf bifurcation initial conditions instability integrable invariant iterations Lagrangian Liapunov exponents Liapunov functional limit cycle linear stability logistic map low-dimensional manifold mass mathematical modes nonlinear obviously one-dimensional orbital dynamics orbits original oscillator parameter particle periodic perturbation phase space physical planets Poincare map potential problem properties pulsation quasiperiodic Regev relevant resonances rotating scales signal solution spatial stability matrix stable stars stellar structure surface of section term theorem theory thermal timescale tion tori torus trajectories transformation turbulence two-dimensional unstable manifolds variables vector velocity zero