historical prologue part 1.systems of nonlinear differential equations chapter 1.geometric approach to differential equations chapter 2.linear systems 2.1.fundamental set of solutions 2.2. constant coefficients：solutions and phase portraits 2.2.1. complex eigenvalues 2.2.2. repeated real eigenvalues 2.2.3.quasiperiodic systems 2.3.nonhomogeneous systems：time-dependent forcing 2.4. applications 2.4.1.mixing fluids 2.4.2. model for malignant tumors 2.4.3.detection of diabetes 2.4.4. electric circuits 2.5.theory and proofs exercises for chapter 2 chapter 3.the flow：solutions of nonlinear equations 3.1. solutions of nonlinear equations 3.1.1. solutions in multiple dimensions .3.2. numerical solutions of differential equations 3.2.1. numerical methods in multiple dimensions 3.3.theory andproofs exercises for chapter 3 chapter 4.phase portraits with emphasis on fixed points 4.1. stability of fixed points 4.2. one.dimensional difierential equations 4.3.two dimensions and nullclines 4.4.linearized stability of fixed points 4.5. competitive populations 4.5.1.three competitive populations 4.6. applications 4.6.1. chemostats 4.6.2. epidemic model 4.7.theory and proofs exercises for chapter 4 chapter 5.phase portraits using energy and other test functions 5.1.predator-prey systems 5.2.undamped forces 5.3.lyapunov functions for damped systems 5.4.limit sets 5.5. gradient systems 5.6. applications 5.6.1. nonlinear oscillators 5.6.2.neural networks 5.7.111eory and proofs exercises for chapter 5 chapter 6.periodic orbits 6.1.definitions and examples 6.2.poincare-bendixson theorem 6.2.1. chemical reaction model 6.3. self-excited oscillator 6.4. andronov-hopfbifurcation 6.5.homoclinic bifurcation to a periodic orbit 6.6. change of area or volume by the flow 6.7. stability of periodic orbits and the poincard map 6.8. applications 6.8.1. chemical oscillation 6.8.2. nonlinear electric circuit 6.8.3.predator-prey system with all andronov-hopf bifurcation 6.9.theory and proofs exercises for chapter 6 chapter 7. chaotic attractors 7.1. attractors 7.2. chaos 7.2.1.sensitive dependence 7.2.2. chaotic attractors 7.3.lorenz system 7.3.1.fixed points for lorenz equations 7.3.2.poincar6 map of lorenz equations 7.4. r6ssler attractor 7.4.1. cantor sets and attractors 7.5.forced oscillator 7.6.lyapunov exponents 7.6.1.numerical calculation of lyapunov exponents 7.7. a test for chaotic attractors 7.8. applications 7.8.1.lorenz system as a model 7.9.theory and proofs exercises for chapter 7 part 2.iteration of functions chapter 8. iteration of functions as dynamics 8.1.one.dimensional maps 8.2.functions with several variables chapter 9.periodic points of one-dimensional maps 9.1.periodic points 9.2. graphical method of i~raton 9.3. stability of periodic points 9.3.1. newton map 9.3.2.fixed and period.2 points for the logistic family 9.4.periodic sinks and schwarzian derivative 9.5.bifurcation of periodic points 9.5.1.the bifurcation diagram for the logistic family 9.6.conjugacy 9.7.applications 9.7.1.capital accumulation 9.7.2.single populmion models 9.7.3.blood cell population model 9.8.theory and proofs exercises for chapter 9 chapter 10.itineraries for 0he-dimensional maps 10.1.periodic points from transition graphs 10.1.1.sharkovskii theorem 10.2.topological transitivity 10.3. sequences of symbols 10.4. sensitive dependence on initial conditions 10.5.cantor sets 10.6.subshifts：piecewise expanding interval maps 10.6.1.counting periodic points for subshifts of finite type 10.7. applications 10.7.1. newton map：nonconvergent orbits 10.7.2. complicated dynamics for populmion growth models 10.8.thetry and proofs exercises for chapter l o chapter 11. invariant sets for olie.dimensional maps 11.1.limit sets 11.2. chaotic attractors 11.2.1.chaotic attractors for expanding maps with discontinuities 11.3.lvapunov exponents 11.3.1.a test for chattie attractors 11.4.measures 11.4.1. general properties of measures 11.4.2.frequency measures 11.4.3.invariant measures for expanding maps 11.5. applications 11.5.1. capital accumulation 11.5.2. chaotic blood cell population 11.6.theory and proofs exercises for chapter 11 chapter 12.periodic points of higher dimensional maps 12.1.dynamics of linear maps 12.2. stability and classification of periodic points 12.3. stable manifolds 12.3.1.numerical calculation ofthe stable manifold 12.3.2. basin boundaries 12.3.3. stable manifolds in higher dimension 12.4.hyperbolic toral automorphisms 12.5. applications 12.5.1.markov chains 12.5.2. newton map in r” 12.5.3. beetle population model 12.5.4. a discrete epidemic model 12.5.5.one-locus genetic model 1 2.6.theory and proofs exercises for chapter 12 chapter 13.invariant sets for higher dimensional maps 13.1.geometric horseshoe 13.1.1. basin boundafies 13.2. symbolic dynamics 13.2.1.correctly aligned rectangle 13.2.2.markov partition 13.2.3.markov partitions for hyperbolic toral automorphisms 13.2.4.shadowing 13.3.homoclinic points and horseshoes 13.4. attractors 13.4.1. chaotic attractors 13.5.lyapunov exponents for maps in higher dimensions 13.5.1.lyapunov exponents from axes of ellipsoids 13.5.2.numerical calculation of lyapunov exponents 13.6. a test for chaotic attractors 13.7.applications 13.7.1. stability ofthe solar system 13.8.theory and proofs exercises for chapter 13 chapter 14. fractals 14.1. box dimension 14.2.dimensions of orbits 14.2.1. c0rrelation dimension 14.2.2.lyapunov dimension 14.3. iterated.function systems 14.3.1. iterated—function systems acting on sets 14.3.2.probabilistic action of iterated—function systems 14.3.3.determining the iterated—function system 14.4.theory and proofs exercises for chapter 14 appendix a.calculus background and notation appendix b.analysis and topology terminology appendix c.matrix algebra appendix d.generic properties bibliography index