We construct a differentiable function () such that the set is a nonempty set of Hausdorff dimension . This answers a question posed by Z. Buczolich.
On construit une fonction différentiable () telle que l’ensemble est non vide et sa dimension de Hausdorff est . C’est une réponse à une question posée par Z. Buczolich.
Keywords: Denjoy–Clarkson property, gradient, Hausdorff measure, infinite game
Mot clés : propriété de Denjoy-Clarkson, gradient, mesure de Hausdorff, jeu infini
@article{AIF_2008__58_2_405_0, author = {Zelen\'y, Miroslav}, title = {The {Denjoy-Clarkson} property with respect to {Hausdorff} measures for the gradient mapping of functions of several variables}, journal = {Annales de l'Institut Fourier}, pages = {405--428}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {2}, year = {2008}, doi = {10.5802/aif.2356}, zbl = {1154.26016}, mrnumber = {2410378}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2356/} }
TY - JOUR AU - Zelený, Miroslav TI - The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables JO - Annales de l'Institut Fourier PY - 2008 SP - 405 EP - 428 VL - 58 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2356/ DO - 10.5802/aif.2356 LA - en ID - AIF_2008__58_2_405_0 ER -
%0 Journal Article %A Zelený, Miroslav %T The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables %J Annales de l'Institut Fourier %D 2008 %P 405-428 %V 58 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2356/ %R 10.5802/aif.2356 %G en %F AIF_2008__58_2_405_0
Zelený, Miroslav. The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables. Annales de l'Institut Fourier, Volume 58 (2008) no. 2, pp. 405-428. doi : 10.5802/aif.2356. http://archive.numdam.org/articles/10.5802/aif.2356/
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