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Science China Mathematics

, Volume 53, Issue 12, pp 3085–3094 | Cite as

Rose solutions with three petals for planar 4-body problems

  • ChunHua Deng
  • ShiQing ZhangEmail author
  • Qing Zhou
Articles

Abstract

For planar Newtonian 4-body problems with equal masses, we use variational methods to prove the existence of a non-collision periodic choreography solution such that all bodies move on a rose-type curve with three petals.

Keywords

4-body problems with Newtonian potentials rose solutions with three petals winding numbers variational minimization methods 

MSC(2000)

34C15 34C25 58E05 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Yangtze Center of Mathematics and College of MathematicsSichuan UniversityChengduChina
  2. 2.Faculty of Mathematics and PhysicsHuaiyin Institute of TechnologyHuai’anChina
  3. 3.Department of MathematicsEast China Normal UniversityShanghaiChina

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