A problem in non-linear Diophantine approximation

被引：1

作者：

Harrap, Stephen ^{[1
]}

Hussain, Mumtaz ^{[2
]}

Kristensen, Simon ^{[3
]}

机构：

[1] Univ Durham, Dept Math Sci, Sci Labs, South Rd, Durham DH1 3LE, England

[2] La Trobe Univ, Dept Math & Stat, POB 199, Bendigo, Vic 3552, Australia

[3] Aarhus Univ, Dept Math, Ny Munkegade 118, DK-8000 Aarhus C, Denmark

来源：

NONLINEARITY | 2018年 / 31卷 / 04期

基金：

澳大利亚研究理事会;

关键词：

non-linear Diophantine approximation; partial differential equations; Hausdorff measure; Hausdorff dimension; Khintchine-Groshev theorem; HAUSDORFF DIMENSION; SOLVABILITY; THEOREM; SETS;

D O I：

10.1088/1361-6544/aaa498

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

引用

页码：1734 / 1756

页数：23

共 50 条

[31] A PROBLEM WITH NON-LINEAR LIMITS
AVRAMESC.C
[J]. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1968, 44 (02): : 179 - &
[32] ON A NON-LINEAR EIGENVALUE PROBLEM
CIPOLATTI, R
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1981, 293 (09): : 455 - 458
[33] ON NON-LINEAR OSCILLATION PROBLEM
MUNOT, PC
MATHUR, R
[J]. JOURNAL OF THE INDIAN INSTITUTE OF SCIENCE SECTION A-ENGINEERING & TECHNOLOGY, 1980, 62 (10): : 167 - 171
[34] A NON-LINEAR SYNTHESIS PROBLEM
HOROWITZ, I
[J]. INTERNATIONAL JOURNAL OF CONTROL, 1980, 32 (05) : 749 - 757
[35] A NON-LINEAR EIGENVALUES PROBLEM
PARTER, SV
PEREYRA, V
[J]. ACTA CIENTIFICA VENEZOLANA, 1970, 21 : 26 - &
[36] A PROBLEM OF DIOPHANTINE APPROXIMATION IN QUATERNIONS
Mahler, Kurt
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1945, 48 : 435 - 466
[37] METRIC PROBLEM FOR DIOPHANTINE APPROXIMATION
DEMATHAN, B
[J]. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1971, 99 (04): : 369 - &
[38] On a mixed problem in Diophantine approximation
Bugeaud, Yann
de Mathan, Bernard
[J]. ACTA ARITHMETICA, 2009, 139 (01) : 65 - 77
[39] ON A NON-LINEAR NOISE PROBLEM
STUMPERS, FLHM
[J]. PHILIPS RESEARCH REPORTS, 1947, 2 (04): : 241 - 259
[40] A problem of Hooley in diophantine approximation
Harman, G
[J]. GLASGOW MATHEMATICAL JOURNAL, 1996, 38 : 299 - 308

← 1 2 3 4 5 →