Class information for:
Level 1: LIMIT CYCLE//ABELIAN INTEGRALS//ISOCHRONOUS CENTER

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
2324 2282 18.3 43%


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

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 2096070 23% 30% 521
2 ABELIAN INTEGRALS authKW 1235278 5% 86% 107
3 ISOCHRONOUS CENTER authKW 794209 3% 93% 64
4 POLYNOMIAL VECTOR FIELDS authKW 706563 3% 81% 65
5 HILBERTS 16TH PROBLEM authKW 643225 2% 96% 50
6 PERIOD FUNCTION authKW 518485 2% 82% 47
7 CENTER FOCUS PROBLEM authKW 508741 2% 98% 39
8 POLYNOMIAL DIFFERENTIAL SYSTEM authKW 488912 2% 89% 41
9 CENTER PROBLEM authKW 447770 2% 71% 47
10 BIFURCATION OF LIMIT CYCLES authKW 383410 1% 87% 33

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 53048 65% 0% 1490
2 Mathematics, Applied 45486 56% 0% 1271
3 Mathematics, Interdisciplinary Applications 4221 10% 0% 231
4 Physics, Mathematical 2523 10% 0% 225
5 Multidisciplinary Sciences 168 2% 0% 39
6 Physics, Multidisciplinary 76 4% 0% 102
7 Mechanics 56 3% 0% 64
8 Automation & Control Systems 8 1% 0% 18
9 Engineering, Mechanical 5 1% 0% 33
10 Physics, Fluids & Plasmas 2 1% 0% 18

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 134754 24% 2% 543
2 MOE LSC 30944 1% 11% 22
3 UMR 6083 SCI TECH 30102 0% 75% 3
4 SCI TECH MATH PHYS THEOR 26758 0% 100% 2
5 THEORET PHYS MATH FIMAT 26758 0% 100% 2
6 LIMB 26093 0% 18% 11
7 ENGN INFORMAT MATEMAT 24134 1% 7% 26
8 UMR 6083 MATH PHYS THEOR 23781 0% 44% 4
9 MATH PHYS THEORUMR 6083 21402 0% 40% 4
10 MATEMAT INFORMAT 18494 1% 6% 25

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 JOURNAL OF DIFFERENTIAL EQUATIONS 122735 11% 4% 257
2 BULLETIN DES SCIENCES MATHEMATIQUES 68689 3% 7% 79
3 QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 68476 1% 20% 26
4 INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 61358 7% 3% 159
5 DIFFERENTIAL EQUATIONS 35742 4% 3% 100
6 JOURNAL OF APPLIED ANALYSIS AND COMPUTATION 31466 1% 9% 26
7 NONLINEARITY 17303 3% 2% 65
8 JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 14731 7% 1% 153
9 NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 13538 5% 1% 111
10 JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 8696 1% 4% 17

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 2096070 23% 30% 521 Search LIMIT+CYCLE Search LIMIT+CYCLE
2 ABELIAN INTEGRALS 1235278 5% 86% 107 Search ABELIAN+INTEGRALS Search ABELIAN+INTEGRALS
3 ISOCHRONOUS CENTER 794209 3% 93% 64 Search ISOCHRONOUS+CENTER Search ISOCHRONOUS+CENTER
4 POLYNOMIAL VECTOR FIELDS 706563 3% 81% 65 Search POLYNOMIAL+VECTOR+FIELDS Search POLYNOMIAL+VECTOR+FIELDS
5 HILBERTS 16TH PROBLEM 643225 2% 96% 50 Search HILBERTS+16TH+PROBLEM Search HILBERTS+16TH+PROBLEM
6 PERIOD FUNCTION 518485 2% 82% 47 Search PERIOD+FUNCTION Search PERIOD+FUNCTION
7 CENTER FOCUS PROBLEM 508741 2% 98% 39 Search CENTER+FOCUS+PROBLEM Search CENTER+FOCUS+PROBLEM
8 POLYNOMIAL DIFFERENTIAL SYSTEM 488912 2% 89% 41 Search POLYNOMIAL+DIFFERENTIAL+SYSTEM Search POLYNOMIAL+DIFFERENTIAL+SYSTEM
9 CENTER PROBLEM 447770 2% 71% 47 Search CENTER+PROBLEM Search CENTER+PROBLEM
10 BIFURCATION OF LIMIT CYCLES 383410 1% 87% 33 Search BIFURCATION+OF+LIMIT+CYCLES Search BIFURCATION+OF+LIMIT+CYCLES

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 -106 145 87% 245
2 LI, CZ , (2012) ABELIAN INTEGRALS AND LIMIT CYCLES.QUALITATIVE THEORY OF DYNAMICAL SYSTEMS. VOL. 11. ISSUE 1. P. 111-128 55 100% 16
3 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 53 85% 25
4 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
5 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
6 SUN, XB , ZHAO, LQ , (2016) PERTURBATIONS OF A CLASS OF HYPER-ELLIPTIC HAMILTONIAN SYSTEMS OF DEGREE SEVEN WITH NILPOTENT SINGULAR POINTS.APPLIED MATHEMATICS AND COMPUTATION. VOL. 289. ISSUE . P. 194 -203 34 92% 0
7 YANG, JH , ZHAO, LQ , (2016) ZEROS OF ABELIAN INTEGRALS FOR A QUARTIC HAMILTONIAN WITH FIGURE-OF-EIGHT LOOP THROUGH A NILPOTENT SADDLE.NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS. VOL. 27. ISSUE . P. 350 -365 31 100% 0
8 AN, YL , HAN, MA , (2015) ON THE NUMBER OF LIMIT CYCLES NEAR A HOMOCLINIC LOOP WITH A NILPOTENT SINGULAR POINT.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 258. ISSUE 9. P. 3194 -3247 34 89% 2
9 ZHAO, YL , (2005) THE PERIOD FUNCTION FOR QUADRATIC INTEGRABLE SYSTEMS WITH CUBIC ORBITS.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 301. ISSUE 2. P. 295-312 40 98% 12
10 HAN, MA , (2012) ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. VOL. 22. ISSUE 12. P. - 36 86% 8

Classes with closest relation at Level 1


Rank Class id link
1 20486 COMPACT INVARIANT SET//FINITE DIMENSIONAL POISSON SYSTEMS//QUASI POLYNOMIAL SYSTEMS
2 19703 NORMAL FORM//UNIQUE NORMAL FORM//FURTHER REDUCTION
3 13113 HOLOMORPHIC FOLIATION//ANALYTIC CLASSIFICATION//LOTKA VOLTERRA DERIVATION
4 23194 MULTIPLE DEVIATING ARGUMENTS//LIENARD SYSTEM//BOUNDEDNESS
5 16933 CANARDS//MIXED MODE OSCILLATIONS//SLOW FAST SYSTEM
6 15600 ORBIT FLIP//INCLINATION FLIP//T POINT
7 5779 BORDER COLLISION BIFURCATION//GRAZING BIFURCATION//IMPACT OSCILLATOR
8 16080 DIFFERENTIAL GALOIS THEORY//NON INTEGRABILITY//DIFFERENTIAL GALOIS GROUP
9 10630 LIE SYSTEM//GEODYSYC//SUPERPOSITION RULE
10 30733 ADJOINT FLOQUET SOLUTIONS//STABILITY IN NONLINEAR APPROXIMATION//PERIODIC PERTURBATIONS

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