Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.
The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.
Editorial Board
Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Chapter
3 Lowering the number of degrees of freedom
pp.：
39 – 49
4 Periodic and conditionally-periodic solutions
pp.：
49 – 54
5 Generalizations
pp.：
54 – 58
Chapter II. Normalization of a Hamiltonian system near a cycle or a torus
pp.：
62 – 68
2 The normal form in a neighbourhood of a periodic solution
pp.：
68 – 76
1 The normal form of a linear Hamiltonian system with periodic coefficients
pp.：
68 – 68
3 The neighbourhood of an invariant torus
pp.：
76 – 89
4 A system with two degrees of freedom
pp.：
89 – 94
Part II. Solutions of the limiting problem (μ = 0)
pp.：
101 – 107
Chapter III. Periodic solutions and arc solutions
pp.：
107 – 109
2 The two-body problem
pp.：
109 – 111
1 Formulation of the restricted three-body problem
pp.：
109 – 109
3 The restricted three-body problem for μ = 0
pp.：
111 – 127
Chapter IV. Properties of arc solutions of the families S and TN
pp.：
146 – 147
2 The structure of the set of characteristics of the families S and TN
pp.：
147 – 166
1 Orbits of the families S
pp.：
147 – 147
3 Values of the Jacobian constant
pp.：
166 – 182
Chapter V. Extrema of the Hamiltonian function on families of arc solutions
pp.：
190 – 192
2 Partial derivatives of the function G
pp.：
192 – 196
1 The function G
pp.：
192 – 192
3 Classification of the segments of the characteristics
pp.：
196 – 200
4 Estimation of the number of intersections of a segment of a characteristic with a level line of the function G
pp.：
200 – 201
5 The domain ρ3
pp.：
201 – 204
6 Conclusion
pp.：
204 – 207
Chapter VI. Trajectories of collisions
pp.：
207 – 208
1 The problem of two bodies P1 and P3
pp.：
208 – 209
2 Trajectories of collision with P2
pp.：
209 – 220
3 Arc solutions with consecutive collisions
pp.：
220 – 236
4 Isolation of critical solutions
pp.：
236 – 242
Part III. Regular generating solutions
pp.：
244 – 247
Chapter VII. Solutions of the second kind
pp.：
247 – 249
1 Sets of periodic solutions
pp.：
249 – 249
2 The restricted three-body problem
pp.：
249 – 256
3 Averaging of the perturbing function
pp.：
256 – 259
4 Computation of generating families
pp.：
259 – 263
5 Concerning the programs
pp.：
263 – 267
6 Other properties of the families EN
pp.：
267 – 268
7 Limits of generating families
pp.：
268 – 269
8 Conditionally-periodic solutions of the second kind
pp.：
269 – 276
Chapter VIII. Solutions of the first kind
pp.：
277 – 280
1 Reduction to the normal form
pp.：
280 – 280
2 Integration of the normal form for rational λ = p̃̃/q̃̃
pp.：
280 – 289
3 Application to the restricted problem
pp.：
289 – 297
4 Conclusion
pp.：
297 – 302
5 The neighbourhood of stationary points
pp.：
302 – 304
Chapter IX. Generating arc solutions from C¯1C¯1
pp.：
309 – 312
1 Generating solutions of collisions with P1
pp.：
312 – 312
2 Computation of families of generating arc solutions
pp.：
312 – 319
3 Asymptotics of families of generating arc solutions
pp.：
319 – 324
4 Concerning periodic solutions with collisions
pp.：
324 – 328
Chapter X. Perturbations of hyperbolic orbits
pp.：
329 – 331
1 The normal form
pp.：
331 – 331
2 Application to the restricted problem
pp.：
331 – 335
Appendix. Tables of generating families and their perturbations
pp.：
339 – 341
Bibliography
pp.：
341 – 361
Author index
pp.：
361 – 371
Subject index
pp.：
371 – 373
The Restricted 3-Body Problem: Plane Periodic Orbits
( De Gruyter Expositions in Mathematics )
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