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Period One Orbits

 

Solving equation (2.10) for x we find two period one solutions,gif

  equation1552

and

  equation1555

The first period one orbit, labeled tex2html_wrap_inline12245 , always remains at the origin, while the location of the second period one orbit, tex2html_wrap_inline12247 , depends on tex2html_wrap_inline11903 . From equation (2.12), the stability of each of these orbits is determined from

  equation1560

and

  equation1563

Clearly, if tex2html_wrap_inline12251 then tex2html_wrap_inline12253 and tex2html_wrap_inline12255 , so the period one orbit tex2html_wrap_inline12245 is stable and tex2html_wrap_inline12247 is unstable. At tex2html_wrap_inline12261 these two orbits collide and exchange stability so that for tex2html_wrap_inline12227 , tex2html_wrap_inline12245 is unstable and tex2html_wrap_inline12247 is stable. For tex2html_wrap_inline12269 , both orbits are unstable.



Nicholas B. Tufillaro
Mon Mar 3 01:58:02 PST 1997