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Dimension and Dynamics for Fractal Recurrent Sets
Author(s) -
Bedford Tim
Publication year - 1986
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-33.1.89
Subject(s) - hausdorff dimension , mathematics , minkowski–bouligand dimension , effective dimension , conjecture , dimension (graph theory) , fractal , packing dimension , fractal dimension , hausdorff space , dimension function , upper and lower bounds , combinatorics , pure mathematics , type (biology) , mathematical analysis , ecology , biology
The fractal ‘recurrent sets’ defined by F. M. Dekking are analysed using subshifts of finite type. We show how Dekking's method is related to a construction due to J. Hutchinson, and prove a conjecture of Dekking concerning conditions under which the best general upper bound for the Hausdorff dimension for recurrent sets is actually equal to the Hausdorff dimension.