First derivative of the period function with applications

Emilio Freire ^[1] ; Armengol Gasull ^[2] ; Antoni Guillamon ^[3]
1. [1] Universidad de Sevilla
  
  Universidad de Sevilla
  
  Sevilla, España
2. [2] Universitat Autònoma de Barcelona
  
  Universitat Autònoma de Barcelona
  
  Barcelona, España
3. [3] Universitat Politècnica de Catalunya
  
  Universitat Politècnica de Catalunya
  
  Barcelona, España
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Localización: XVII Congreso de Ecuaciones Diferenciales y Aplicaciones ; VII Congreso de Matemática Aplicada: Salamanca, 14-28 septiembre 2001 / coord. por Luis Ferragut Canals, Anastasio Pedro Santos Yanguas, 2001, ISBN 8469961446, págs. 527-528
Idioma: inglés
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Resumen
- In the present paper, inspired in the geometrical ideas involved in the Lie bracket, we give a method to prove that some centres have either an increasing or a decreasing period function. This method is based on a formula for computing the derivative of the period function, which is obtained from the knowledge of the set of normalizers of the centre. The following Theorem is the main result of our work.