Class information for:
Level 1: DIOPHANTINE APPROXIMATION//METRIC DIOPHANTINE APPROXIMATION//FORMAL LAURENT SERIES

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
8444 1253 18.8 36%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
205 3       MATHEMATICS//JOURNAL OF NUMBER THEORY//ACTA ARITHMETICA 52461
1098 2             HAUSDORFF DIMENSION//ERGODIC THEORY AND DYNAMICAL SYSTEMS//MATHEMATICS 9817
8444 1                   DIOPHANTINE APPROXIMATION//METRIC DIOPHANTINE APPROXIMATION//FORMAL LAURENT SERIES 1253

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 DIOPHANTINE APPROXIMATION authKW 584803 7% 29% 83
2 METRIC DIOPHANTINE APPROXIMATION authKW 219308 1% 75% 12
3 FORMAL LAURENT SERIES authKW 219302 1% 60% 15
4 SCHMIDTS GAME authKW 194945 1% 100% 8
5 INHOMOGENEOUS DIOPHANTINE APPROXIMATION authKW 187443 1% 77% 10
6 CURLICUES authKW 170577 1% 100% 7
7 HAUSDORFF DIMENSION authKW 144390 6% 7% 80
8 FLOWS ON HOMOGENEOUS SPACES authKW 121841 0% 100% 5
9 RATNERS THEOREM authKW 121841 0% 100% 5
10 UNIPOTENT FLOWS authKW 121841 0% 100% 5

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with term
in class
1 Mathematics 62575 95% 0% 1189
2 Mathematics, Applied 3053 20% 0% 256
3 Physics, Mathematical 29 2% 0% 26
4 Multidisciplinary Sciences 21 1% 0% 12
5 Statistics & Probability -0 0% 0% 6
6 Computer Science, Theory & Methods -1 0% 0% 6
7 Automation & Control Systems -2 0% 0% 2
8 Computer Science, Hardware & Architecture -2 0% 0% 1
9 Mathematics, Interdisciplinary Applications -4 0% 0% 1
10 Computer Science, Software Engineering -5 0% 0% 1

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MATH EQUIPE TOPOL DYNAM 48736 0% 100% 2
2 BASIS COMMUN 24368 0% 100% 1
3 CNRSEQUIPE TOPOL DYNAM 24368 0% 100% 1
4 CNRSUFR MATH PURE PL 24368 0% 100% 1
5 EQUIPE THEORIE ERGOD SYST DYNAMUMR 7599 24368 0% 100% 1
6 FOR GRP KONVEXE DISKRETE GEOMETR 24368 0% 100% 1
7 ITS CROSS 24368 0% 100% 1
8 LAMA 61 24368 0% 100% 1
9 M UMR CNRS 12 7373 24368 0% 100% 1
10 MATH INFORMAT HBEREICH 3 24368 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 ERGODIC THEORY AND DYNAMICAL SYSTEMS 66516 6% 3% 81
2 ACTA ARITHMETICA 54682 7% 3% 85
3 JOURNAL OF MODERN DYNAMICS 42903 2% 9% 20
4 DUKE MATHEMATICAL JOURNAL 23386 4% 2% 53
5 JOURNAL OF NUMBER THEORY 21838 5% 1% 65
6 GEOMETRIC AND FUNCTIONAL ANALYSIS 15683 2% 2% 26
7 MATHEMATIKA 14841 2% 3% 23
8 INTERNATIONAL JOURNAL OF NUMBER THEORY 13549 2% 2% 25
9 MONATSHEFTE FUR MATHEMATIK 10983 3% 1% 32
10 ISRAEL JOURNAL OF MATHEMATICS 10869 3% 1% 41

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 DIOPHANTINE APPROXIMATION 584803 7% 29% 83 Search DIOPHANTINE+APPROXIMATION Search DIOPHANTINE+APPROXIMATION
2 METRIC DIOPHANTINE APPROXIMATION 219308 1% 75% 12 Search METRIC+DIOPHANTINE+APPROXIMATION Search METRIC+DIOPHANTINE+APPROXIMATION
3 FORMAL LAURENT SERIES 219302 1% 60% 15 Search FORMAL+LAURENT+SERIES Search FORMAL+LAURENT+SERIES
4 SCHMIDTS GAME 194945 1% 100% 8 Search SCHMIDTS+GAME Search SCHMIDTS+GAME
5 INHOMOGENEOUS DIOPHANTINE APPROXIMATION 187443 1% 77% 10 Search INHOMOGENEOUS+DIOPHANTINE+APPROXIMATION Search INHOMOGENEOUS+DIOPHANTINE+APPROXIMATION
6 CURLICUES 170577 1% 100% 7 Search CURLICUES Search CURLICUES
7 HAUSDORFF DIMENSION 144390 6% 7% 80 Search HAUSDORFF+DIMENSION Search HAUSDORFF+DIMENSION
8 FLOWS ON HOMOGENEOUS SPACES 121841 0% 100% 5 Search FLOWS+ON+HOMOGENEOUS+SPACES Search FLOWS+ON+HOMOGENEOUS+SPACES
9 RATNERS THEOREM 121841 0% 100% 5 Search RATNERS+THEOREM Search RATNERS+THEOREM
10 UNIPOTENT FLOWS 121841 0% 100% 5 Search UNIPOTENT+FLOWS Search UNIPOTENT+FLOWS

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 BADZIAHIN, D , BERESNEVICH, V , VELANI, S , (2013) INHOMOGENEOUS THEORY OF DUAL DIOPHANTINE APPROXIMATION ON MANIFOLDS.ADVANCES IN MATHEMATICS. VOL. 232. ISSUE 1. P. 1-35 33 100% 4
2 STARKOV, AN , (1997) NEW PROGRESS IN THE THEORY OF HOMOGENEOUS FLOWS.RUSSIAN MATHEMATICAL SURVEYS. VOL. 52. ISSUE 4. P. 721 -818 55 89% 2
3 EINSIEDLER, M , MARGULIS, G , VENKATESH, A , (2009) EFFECTIVE EQUIDISTRIBUTION FOR CLOSED ORBITS OF SEMISIMPLE GROUPS ON HOMOGENEOUS SPACES.INVENTIONES MATHEMATICAE. VOL. 177. ISSUE 1. P. 137-212 37 86% 17
4 GORODNIK, A , NEVO, A , (2014) ERGODIC THEORY AND THE DUALITY PRINCIPLE ON HOMOGENEOUS SPACES.GEOMETRIC AND FUNCTIONAL ANALYSIS. VOL. 24. ISSUE 1. P. 159-244 28 90% 0
5 EINSIEDLER, M , LINDENSTRAUSS, E , (2015) ON MEASURES INVARIANT UNDER TORI ON QUOTIENTS OF SEMISIMPLE GROUPS.ANNALS OF MATHEMATICS. VOL. 181. ISSUE 3. P. 993 -1031 22 96% 1
6 DANI, SG , (2008) DIOPHANTINE APPROXIMATION AND DYNAMICS OF UNIPOTENT FLOWS ON HOMOGENEOUS SPACES.PURE AND APPLIED MATHEMATICS QUARTERLY. VOL. 4. ISSUE 1. P. 147-166 25 100% 0
7 BERESNEVICH, V , VELANI, S , (2010) AN INHOMOGENEOUS TRANSFERENCE PRINCIPLE AND DIOPHANTINE APPROXIMATION.PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. VOL. 101. ISSUE . P. 821 -851 23 100% 6
8 KLEINBOCK, D , MARGULIS, G , WANG, JB , (2010) METRIC DIOPHANTINE APPROXIMATION FOR SYSTEMS OF LINEAR FORMS VIA DYNAMICS.INTERNATIONAL JOURNAL OF NUMBER THEORY. VOL. 6. ISSUE 5. P. 1139-1168 24 96% 4
9 CELLAROSI, F , MARKLOF, J , (2016) QUADRATIC WEYL SUMS, AUTOMORPHIC FUNCTIONS AND INVARIANCE PRINCIPLES.PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY. VOL. 113. ISSUE . P. 775 -828 25 81% 0
10 BERESNEVICH, V , (2012) RATIONAL POINTS NEAR MANIFOLDS AND METRIC DIOPHANTINE APPROXIMATION.ANNALS OF MATHEMATICS. VOL. 175. ISSUE 1. P. 187-235 22 92% 10

Classes with closest relation at Level 1


Rank Class id link
1 23249 APOLLONIAN PACKING//AXIAL FUNCTIONS//BABAIS CONJECTURE
2 24058 ALGEBRAIC ENTROPY//ALGEBRAIC ACTION//MEAN DIMENSION
3 33651 NORMAL NUMBERS//CANTOR SERIES//POLYNOMIAL TIME RANDOMNESS
4 11113 HARMONIC MANIFOLDS//ASYMPTOTICALLY HARMONIC MANIFOLDS//BOUNDARY RIGIDITY
5 19134 HECKE GROUPS//SUBORBITAL GRAPHS//EXTENDED HECKE GROUP
6 14899 TRANSLATION SURFACE//INTERVAL EXCHANGE TRANSFORMATION//VEECH GROUPS
7 2811 HAUSDORFF DIMENSION//SELF SIMILAR SET//ITERATED FUNCTION SYSTEM
8 28629 MATH INVEST CRYSTALLOG MINERAL PETROG//PLATINUM GRP ELEMENTS ORE GENESIS//PRODUCT OF LINEAR FORMS
9 28473 KLEIN POLYHEDRON//MULTIDIMENSIONAL CONTINUED FRACTION//SIMULTANEOUS DIOPHANTINE APPROXIMATIONS
10 28866 NOWHERE DIFFERENTIABLE FUNCTION//SINGULAR FUNCTIONS//TAKAGIS FUNCTION

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