On the helix equation

Mohamed Hmissi; Imene Ben Salah; Hajer Taouil

On the helix equation

Mohamed Hmissi; Imene Ben Salah; Hajer Taouil

ESAIM: Proceedings (2012)

Volume: 36, page 197-208
ISSN: 1270-900X

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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{matrix} H (0,ω) = 0; H (s + t,ω) = H (s, Φ (t,ω)) + H (t,ω) \end{matrix}

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.

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Hmissi, Mohamed, Ben Salah, Imene, and Taouil, Hajer. Fournier-Prunaret, D., Gardini, L., and Reich, L., eds. " On the helix equation ." ESAIM: Proceedings 36 (2012): 197-208. <http://eudml.org/doc/251284>.

@article{Hmissi2012,
abstract = {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\} 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.},
author = {Hmissi, Mohamed, Ben Salah, Imene, Taouil, Hajer},
editor = {Fournier-Prunaret, D., Gardini, L., Reich, L.},
journal = {ESAIM: Proceedings},
keywords = {translation equation; helix equation; Wiener helix; cocycle equation},
language = {eng},
month = {8},
pages = {197-208},
publisher = {EDP Sciences},
title = { On the helix equation },
url = {http://eudml.org/doc/251284},
volume = {36},
year = {2012},
}

TY - JOUR
AU - Hmissi, Mohamed
AU - Ben Salah, Imene
AU - Taouil, Hajer
AU - Fournier-Prunaret, D.
AU - Gardini, L.
AU - Reich, L.
TI - On the helix equation
JO - ESAIM: Proceedings
DA - 2012/8//
PB - EDP Sciences
VL - 36
SP - 197
EP - 208
AB - 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} 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.
LA - eng
KW - translation equation; helix equation; Wiener helix; cocycle equation
UR - http://eudml.org/doc/251284
ER -

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