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140122 ||| eng |
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|a 9789401592994
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|a Pei-Chu Hu
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|a Differentiable and Complex Dynamics of Several Variables
|h Elektronische Ressource
|c by Pei-Chu Hu, Chung-Chun Yang
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| 250 |
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|a 1st ed. 1999
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| 260 |
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|a Dordrecht
|b Springer Netherlands
|c 1999, 1999
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| 300 |
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|a X, 342 p
|b online resource
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|a 1 Fatou-Julia type theory -- 2 Ergodic theorems and invariant sets -- 3 Hyperbolicity in differentiable dynamics -- 4 Some topics in dynamics -- 5 Hyperbolicity in complex dynamics -- 6 Iteration theory on ?m -- 7 Complex dynamics in ?m -- A Foundations of differentiable dynamics -- B Foundations of complex dynamics
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| 653 |
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|a Several Complex Variables and Analytic Spaces
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Measure theory
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| 653 |
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|a Functions of complex variables
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| 653 |
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|a Manifolds (Mathematics)
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| 653 |
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|a Differential Geometry
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| 653 |
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|a Measure and Integration
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| 653 |
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|a Differential Equations
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| 653 |
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|a Global analysis (Mathematics)
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| 653 |
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|a Global Analysis and Analysis on Manifolds
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| 653 |
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|a Differential equations
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| 700 |
1 |
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|a Chung-Chun Yang
|e [author]
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Mathematics and Its Applications
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| 028 |
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|a 10.1007/978-94-015-9299-4
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| 856 |
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|u https://doi.org/10.1007/978-94-015-9299-4?nosfx=y
|x Verlag
|3 Volltext
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|a 514.74
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| 520 |
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|a 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.
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