Differentiable and Complex Dynamics of Several Variables

1. Front Matter

   Pages i-ix

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2. Fatou-Julia type theory

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 1-37

3. Ergodic theorems and invariant sets

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 39-62

4. Hyperbolicity in differentiable dynamics

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 63-97

5. Some topics in dynamics

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 99-136

6. Hyperbolicity in complex dynamics

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 137-177

7. Iteration theory on ℙ^m

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 179-202

8. Complex dynamics in ℂ^m

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 203-232

9. Foundations of differentiable dynamics

   • Pei-Chu Hu, Chung-Chun Yang

   Pages 233-274

10. Foundations of complex dynamics

    • Pei-Chu Hu, Chung-Chun Yang

    Pages 275-318

11. Back Matter

    Pages 319-341

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The development of dynamics theory began with the work of Isaac Newton. In his theory the most basic law of classical mechanics is f = ma, which describes the motion n in IR. of a point of mass m under the action of a force f by giving the acceleration a. If n the position of the point is taken to be a point x E IR. , and if the force f is supposed to be a function of x only, Newton's Law is a description in terms of a second-order ordinary differential equation: J2x m dt = f(x). 2 It makes sense to reduce the equations to first order by defining the velo city as an extra n independent variable by v = :i; = ~~ E IR. . Then x = v, mv = f(x). L. Euler, J. L. Lagrange and others studied mechanics by means of an analytical method called analytical dynamics. Whenever the force f is represented by a gradient vector field f = - \lU of the potential energy U, and denotes the difference of the kinetic energy and the potential energy by 1 L(x,v) = 2'm(v,v) - U(x), the Newton equation of motion is reduced to the Euler-Lagrange equation ~~ are used as the variables, the Euler-Lagrange equation can be If the momenta y written as . 8L y= 8x' Further, W. R.

• analysis on manifolds
• differential equation
• differential geometry
• dynamical systems
• global analysis
• integration
• manifold
• partial differential equation
• partial differential equations

• Shandong University, Jinan, China

  Pei-Chu Hu

• The Hong Kong University of Science and Technology, Kowloon, Hong Kong

  Chung-Chun Yang

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