Geodesic
On the helix equation
Mohamed Hmissi1 ; Imene Ben Salah1 ; Hajer Taouil1
1 Département de Mathématiques, Faculté des Sciences de Tunis, Université de Tunis Elmanar, TN-2092 Elmanar, Tunis, Tunisia
ESAIM. Proceedings, Tome 36 (2012), pp. 197-208.

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This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω) ↦ H(t, ω) of the helix equation \begin{eqnarray} H(0,\o)=0; \quad H(s+t,\o)= H(s,\Phi(t,\o)) +H(t,\o)\nonumber \end{eqnarray} H ( 0 ,ω ) = 0 ;   H ( s + t,ω ) = H ( s, Φ ( t,ω ) ) + H ( t,ω ) where Φ : ℝ × Ω → Ω, (t, ω) ↦ Φ(t, ω) is a dynamical system on a measurable space (Ω, ℱ).More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated.
DOI : 10.1051/proc/201236016

Mohamed Hmissi 1 ; Imene Ben Salah 1 ; Hajer Taouil 1

1 Département de Mathématiques, Faculté des Sciences de Tunis, Université de Tunis Elmanar, TN-2092 Elmanar, Tunis, Tunisia 
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     title = {On the helix equation},
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Mohamed Hmissi; Imene Ben Salah; Hajer Taouil. On the helix equation. ESAIM. Proceedings, Tome 36 (2012), pp. 197-208. doi : 10.1051/proc/201236016. http://geodesic.mathdoc.fr/articles/10.1051/proc/201236016/

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