Class information for:
Level 2: LIMIT CYCLE//ABELIAN INTEGRALS//ISOCHRONOUS CENTER

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
1529 7469 19.8 41%


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
10 4 OPTICS//PHYSICS, PARTICLES & FIELDS//PHYSICS, MULTIDISCIPLINARY 1131262
299 3       PHYSICS, MATHEMATICAL//JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS//BACKLUND TRANSFORMATION 41113
1529 2             LIMIT CYCLE//ABELIAN INTEGRALS//ISOCHRONOUS CENTER 7469
2324 1                   LIMIT CYCLE//ABELIAN INTEGRALS//ISOCHRONOUS CENTER 2282
9876 1                   KOWALEVSKI TOP//INTEGRABLE HAMILTONIAN SYSTEMS//ISOSPECTRAL FLOW 1112
10630 1                   LIE SYSTEM//GEODYSYC//SUPERPOSITION RULE 1047
12667 1                   SUPERINTEGRABILITY//SUPERINTEGRABLE SYSTEMS//STACKEL SYSTEMS 889
16080 1                   DIFFERENTIAL GALOIS THEORY//NON INTEGRABILITY//DIFFERENTIAL GALOIS GROUP 674
20486 1                   COMPACT INVARIANT SET//FINITE DIMENSIONAL POISSON SYSTEMS//QUASI POLYNOMIAL SYSTEMS 458
23019 1                   GENERALIZED RIEMANNIAN SPACE//GEODESIC MAPPING//GEODESICALLY EQUIVALENT METRICS 361
24086 1                   UMR 8101//HAMILTONIAN MONODROMY//ENERGY MOMENTUM MAP 324
28344 1                   SOLVABLE DYNAMICAL SYSTEMS//ISOCHRONOUS DYNAMICAL SYSTEMS//INTEGRABLE DYNAMICAL SYSTEMS 209
34270 1                   SZEBEHELYS EQUATION//INVERSE PROBLEM OF DYNAMICS//MONOPARAMETRIC FAMILIES OF ORBITS 113

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 LIMIT CYCLE authKW 654519 7% 30% 527
2 ABELIAN INTEGRALS authKW 377265 1% 86% 107
3 ISOCHRONOUS CENTER authKW 242565 1% 93% 64
4 POLYNOMIAL VECTOR FIELDS authKW 236170 1% 85% 68
5 HILBERTS 16TH PROBLEM authKW 196455 1% 96% 50
6 POLYNOMIAL DIFFERENTIAL SYSTEM authKW 179886 1% 98% 45
7 PERIOD FUNCTION authKW 158347 1% 82% 47
8 CENTER FOCUS PROBLEM authKW 155381 1% 98% 39
9 CENTER PROBLEM authKW 136742 1% 71% 47
10 FIRST INTEGRAL authKW 133838 1% 34% 97

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 Physics, Mathematical 93121 31% 1% 2341
2 Mathematics, Applied 62874 37% 1% 2742
3 Mathematics 54650 37% 1% 2793
4 Physics, Multidisciplinary 8074 16% 0% 1224
5 Mathematics, Interdisciplinary Applications 5099 6% 0% 474
6 Mechanics 2141 7% 0% 511
7 Multidisciplinary Sciences 223 1% 0% 89
8 Physics, Particles & Fields 99 2% 0% 164
9 Physics, Nuclear 51 2% 0% 121
10 Physics, Fluids & Plasmas 50 1% 0% 90

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 MATEMAT 72140 10% 2% 723
2 GEODYSYC 54080 0% 88% 15
3 DIFFERENTIAL EQUAT CONTINUUM MECH PLICAT 33498 1% 16% 52
4 MATH COMPUTAT PHYS 29693 0% 36% 20
5 GSIB 29057 0% 89% 8
6 UMR 8101 27133 0% 27% 25
7 MATH 25992 23% 0% 1693
8 DST NRF EXCELLENCE MATH STAT SCI 23557 0% 38% 15
9 RECH MATH 19235 1% 7% 65
10 SEZ ROMA 18426 2% 4% 113

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 REGULAR & CHAOTIC DYNAMICS 116573 2% 21% 139
2 JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS 115767 2% 16% 174
3 JOURNAL OF DIFFERENTIAL EQUATIONS 53121 4% 4% 307
4 JOURNAL OF MATHEMATICAL PHYSICS 45191 6% 3% 422
5 INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 31833 3% 4% 208
6 BULLETIN DES SCIENCES MATHEMATIQUES 31519 1% 8% 97
7 SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 30661 1% 8% 95
8 QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 25990 0% 22% 29
9 JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 22879 4% 2% 300
10 JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 22196 3% 3% 217

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 LIMIT CYCLE 654519 7% 30% 527 Search LIMIT+CYCLE Search LIMIT+CYCLE
2 ABELIAN INTEGRALS 377265 1% 86% 107 Search ABELIAN+INTEGRALS Search ABELIAN+INTEGRALS
3 ISOCHRONOUS CENTER 242565 1% 93% 64 Search ISOCHRONOUS+CENTER Search ISOCHRONOUS+CENTER
4 POLYNOMIAL VECTOR FIELDS 236170 1% 85% 68 Search POLYNOMIAL+VECTOR+FIELDS Search POLYNOMIAL+VECTOR+FIELDS
5 HILBERTS 16TH PROBLEM 196455 1% 96% 50 Search HILBERTS+16TH+PROBLEM Search HILBERTS+16TH+PROBLEM
6 POLYNOMIAL DIFFERENTIAL SYSTEM 179886 1% 98% 45 Search POLYNOMIAL+DIFFERENTIAL+SYSTEM Search POLYNOMIAL+DIFFERENTIAL+SYSTEM
7 PERIOD FUNCTION 158347 1% 82% 47 Search PERIOD+FUNCTION Search PERIOD+FUNCTION
8 CENTER FOCUS PROBLEM 155381 1% 98% 39 Search CENTER+FOCUS+PROBLEM Search CENTER+FOCUS+PROBLEM
9 CENTER PROBLEM 136742 1% 71% 47 Search CENTER+PROBLEM Search CENTER+PROBLEM
10 FIRST INTEGRAL 133838 1% 34% 97 Search FIRST+INTEGRAL Search FIRST+INTEGRAL

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 LI, JB , (2003) HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. VOL. 13. ISSUE 1. P. 47 -106 146 88% 245
2 MILLER, W , POST, S , WINTERNITZ, P , (2013) CLASSICAL AND QUANTUM SUPERINTEGRABILITY WITH APPLICATIONS.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. VOL. 46. ISSUE 42. P. - 102 82% 49
3 LI, CZ , (2012) ABELIAN INTEGRALS AND LIMIT CYCLES.QUALITATIVE THEORY OF DYNAMICAL SYSTEMS. VOL. 11. ISSUE 1. P. 111-128 55 100% 16
4 RANADA, MF , (2013) HIGHER ORDER SUPERINTEGRABILITY OF SEPARABLE POTENTIALS WITH A NEW APPROACH TO THE POST-WINTERNITZ SYSTEM.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. VOL. 46. ISSUE 12. P. - 49 96% 7
5 GINE, J , (2007) ON SOME OPEN PROBLEMS IN PLANAR DIFFERENTIAL SYSTEMS AND HILBERT'S 16TH PROBLEM.CHAOS SOLITONS & FRACTALS. VOL. 31. ISSUE 5. P. 1118 -1134 57 92% 25
6 RANADA, MF , (2015) SUPERINTEGRABLE DEFORMATIONS OF SUPERINTEGRABLE SYSTEMS: QUADRATIC SUPERINTEGRABILITY AND HIGHER-ORDER SUPERINTEGRABILITY.JOURNAL OF MATHEMATICAL PHYSICS. VOL. 56. ISSUE 4. P. - 47 92% 1
7 POST, S , WINTERNITZ, P , (2015) GENERAL NTH ORDER INTEGRALS OF MOTION IN THE EUCLIDEAN PLANE.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. VOL. 48. ISSUE 40. P. - 40 95% 2
8 BRISKIN, M , ROYTVARF, N , YOMDIN, Y , (2010) CENTER CONDITIONS AT INFINITY FOR ABEL DIFFERENTIAL EQUATIONS.ANNALS OF MATHEMATICS. VOL. 172. ISSUE 1. P. 437 -483 40 98% 23
9 CARINENA, JF , RANADA, MF , SANTANDER, M , (2011) THE QUANTUM FREE PARTICLE ON SPHERICAL AND HYPERBOLIC SPACES: A CURVATURE DEPENDENT APPROACH.JOURNAL OF MATHEMATICAL PHYSICS. VOL. 52. ISSUE 7. P. - 48 80% 10
10 BRISKIN, M , YOMDIN, Y , (2005) TANGENTIAL VERSION OF HILBERT 16TH PROBLEM FOR THE ABEL EQUATION.MOSCOW MATHEMATICAL JOURNAL. VOL. 5. ISSUE 1. P. 23-53 46 98% 9

Classes with closest relation at Level 2


Rank Class id link
1 2480 LIE ALGEBROIDS//JOURNAL OF GEOMETRIC MECHANICS//DIRAC STRUCTURES
2 2273 CONSERVED QUANTITY//GEOMETRIC PHASE//MEI SYMMETRY
3 127 PHYSICS, MATHEMATICAL//BACKLUND TRANSFORMATION//SOLITON SOLUTION
4 2787 BIFURCATION CONTROL//NORMAL FORM//UNIT IND AUTOMAT
5 4184 TABLE TENNIS ROBOT//SPINNING BALL//AMERICAN JOURNAL OF PHYSICS
6 3698 RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS//CHAIR QUANTUM STAT FIELD THEORY//BOSE EINSTEIN DISTRIBUTION
7 2483 SOLITONS MONOPOLES AND INSTANTONS//G2 STRUCTURE//WILLIAM I FINE THEORET PHYS
8 820 PT SYMMETRY//DIRAC EQUATION//NIKIFOROV UVAROV METHOD
9 1519 STOCHASTIC AVERAGING//BORDER COLLISION BIFURCATION//NONLINEAR ENERGY SINK
10 1097 PHYSICS, MATHEMATICAL//JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL//BETHE ANSATZ

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