𝔖 Bobbio Scriptorium
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Hyperbolicity of Closed Orbits Determined by One Function

✍ Scribed by O. Langer

Publisher
John Wiley and Sons
Year
1984
Tongue
English
Weight
902 KB
Volume
118
Category
Article
ISSN
0025-584X

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✦ Synopsis

Flows on R" are considered whose vector fields can be represented by a composition

Rfl + R1 --f R". Thus these vector fields and flows are determined by elements of Cr(Rn, R)

x U ( R , R"). Vector fields of this and similar kind occur in ecological models. In general these flows have no rest point. We consider the problem how general is the property that closed orbits are hyperbolic and therefore stable under perturbations of the vector field. It is shown that in the restricted class of the vector fields described above generically all closed orbits are hyperbolic. This means that the theorem of KUPKA and SYALE holds partielly in this situation.

') (r,(h)) dh where the w(hi) are regarded as 8W(h) wectws in Rn-l x {0} c R".

πŸ“œ SIMILAR VOLUMES

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For a hyperbolic rational map R of the Riemann sphere of degree d 2 2, restricted to its . l d b set J(R), we define a %eta function C R ( d ) , which counts the prepenodic orbib of R, according to Lhe weight function IR'I : J(R) -+ C . An analysis of the analytic domain of ( ~( d ) , using techniqu