Class information for:
Level 1: NORMAL FORM//UNIQUE NORMAL FORM//FURTHER REDUCTION

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
19703 493 18.9 34%


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
9 4 COMPUTER SCIENCE, THEORY & METHODS//COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE//COMPUTER SCIENCE, INFORMATION SYSTEMS 1247339
74 3       AUTOMATION & CONTROL SYSTEMS//IEEE TRANSACTIONS ON AUTOMATIC CONTROL//AUTOMATICA 82579
2787 2             BIFURCATION CONTROL//NORMAL FORM//UNIT IND AUTOMAT 3108
19703 1                   NORMAL FORM//UNIQUE NORMAL FORM//FURTHER REDUCTION 493

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 NORMAL FORM authKW 402993 16% 8% 81
2 UNIQUE NORMAL FORM authKW 379361 1% 88% 7
3 FURTHER REDUCTION authKW 247747 1% 100% 4
4 NILPOTENT LINEAR PART authKW 247747 1% 100% 4
5 PARAMETRIC NORMAL FORM authKW 247747 1% 100% 4
6 THE SIMPLEST NORMAL FORM authKW 247747 1% 100% 4
7 CONVENTIONAL NORMAL FORM authKW 185810 1% 100% 3
8 FORMAL ORBITAL NORMAL FORM authKW 185810 1% 100% 3
9 POINCARE DULAC NORMAL FORM authKW 140760 1% 45% 5
10 HOPF ZERO SINGULARITY authKW 139356 1% 75% 3

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, Applied 5991 44% 0% 216
2 Mathematics 3195 35% 0% 174
3 Mechanics 2099 23% 0% 114
4 Physics, Mathematical 1374 15% 0% 75
5 Mathematics, Interdisciplinary Applications 733 9% 0% 45
6 Engineering, Mechanical 381 10% 0% 48
7 Acoustics 314 5% 0% 25
8 Physics, Multidisciplinary 118 9% 0% 43
9 Engineering, General 107 4% 0% 20
10 Automation & Control Systems 48 2% 0% 12

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 AGAT UMR 8524 82581 0% 67% 2
2 FAEA 82581 0% 67% 2
3 INVEST INGN ELECT ALFREDO DESAGES UNS CONICE 82581 0% 67% 2
4 ESCUELA POLITECHN SUPER 61937 0% 100% 1
5 INGN ELECT COMPUADORAS 61937 0% 100% 1
6 MATEMAT INFORMAT GRP MECAN ESPACIAL 61937 0% 100% 1
7 MATH COMP SCI PLICAT 61937 0% 100% 1
8 MTH EMILE PICARD 61937 0% 100% 1
9 UMR 5030GTA 61937 0% 100% 1
10 JA DIEUDONNE UMR 6621 49547 0% 40% 2

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 INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 7582 5% 0% 26
2 JOURNAL OF DIFFERENTIAL EQUATIONS 4523 5% 0% 23
3 DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS 4403 2% 1% 8
4 APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION 4124 3% 0% 14
5 DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES B-APPLICATIONS & ALGORITHMS 3318 1% 1% 7
6 INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 3187 3% 0% 13
7 ANNALES DE L INSTITUT FOURIER 2838 2% 0% 10
8 NONLINEARITY 2289 2% 0% 11
9 REGULAR & CHAOTIC DYNAMICS 2281 1% 1% 5
10 NONLINEAR DYNAMICS 2093 3% 0% 13

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 NORMAL FORM 402993 16% 8% 81 Search NORMAL+FORM Search NORMAL+FORM
2 UNIQUE NORMAL FORM 379361 1% 88% 7 Search UNIQUE+NORMAL+FORM Search UNIQUE+NORMAL+FORM
3 FURTHER REDUCTION 247747 1% 100% 4 Search FURTHER+REDUCTION Search FURTHER+REDUCTION
4 NILPOTENT LINEAR PART 247747 1% 100% 4 Search NILPOTENT+LINEAR+PART Search NILPOTENT+LINEAR+PART
5 PARAMETRIC NORMAL FORM 247747 1% 100% 4 Search PARAMETRIC+NORMAL+FORM Search PARAMETRIC+NORMAL+FORM
6 THE SIMPLEST NORMAL FORM 247747 1% 100% 4 Search THE+SIMPLEST+NORMAL+FORM Search THE+SIMPLEST+NORMAL+FORM
7 CONVENTIONAL NORMAL FORM 185810 1% 100% 3 Search CONVENTIONAL+NORMAL+FORM Search CONVENTIONAL+NORMAL+FORM
8 FORMAL ORBITAL NORMAL FORM 185810 1% 100% 3 Search FORMAL+ORBITAL+NORMAL+FORM Search FORMAL+ORBITAL+NORMAL+FORM
9 POINCARE DULAC NORMAL FORM 140760 1% 45% 5 Search POINCARE+DULAC+NORMAL+FORM Search POINCARE+DULAC+NORMAL+FORM
10 HOPF ZERO SINGULARITY 139356 1% 75% 3 Search HOPF+ZERO+SINGULARITY Search HOPF+ZERO+SINGULARITY

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 GAZOR, M , YU, P , (2010) FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. VOL. 20. ISSUE 11. P. 3487 -3515 27 100% 1
2 GAZOR, M , MOAZENI, M , (2015) PARAMETRIC NORMAL FORMS FOR BOGDANOV-TAKENS SINGULARITY; THE GENERALIZED SADDLE-NODE CASE.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. VOL. 35. ISSUE 1. P. 205 -224 23 88% 0
3 YU, P , LEUNG, AYT , (2007) NORMAL FORMS OF VECTOR FIELDS WITH PERTURBATION PARAMETERS AND THEIR APPLICATION.CHAOS SOLITONS & FRACTALS. VOL. 34. ISSUE 2. P. 564-579 23 100% 4
4 GAZOR, M , MOKHTARI, F , SANDERS, JA , (2013) NORMAL FORMS FOR HOPF-ZERO SINGULARITIES WITH NONCONSERVATIVE NONLINEAR PART.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 254. ISSUE 3. P. 1571-1581 19 95% 3
5 GAZOR, H , (2013) NORMAL FORM OF BOGDANOV-TAKENS: STYLES AND A HYPERNORMALIZATION METHOD.NONLINEAR DYNAMICS. VOL. 72. ISSUE 3. P. 499-505 20 87% 1
6 YU, P , GAZOR, M , (2008) INFINITE ORDER PARAMETRIC NORMAL FORM OF HOPF SINGULARITY.INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. VOL. 18. ISSUE 11. P. 3393 -3408 22 88% 3
7 SANDERS, JA , (2003) NORMAL FORM THEORY AND SPECTRAL SEQUENCES.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 192. ISSUE 2. P. 536-552 21 100% 23
8 GAZOR, M , YU, P , (2012) SPECTRAL SEQUENCES AND PARAMETRIC NORMAL FORMS.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 252. ISSUE 2. P. 1003 -1031 19 83% 6
9 GAZOR, M , MOKHTARI, F , (2013) VOLUME-PRESERVING NORMAL FORMS OF HOPF-ZERO SINGULARITY.NONLINEARITY. VOL. 26. ISSUE 10. P. 2809-2832 22 71% 0
10 YU, P , LEUNG, AYT , (2003) THE SIMPLEST NORMAL FORM OF HOPF BIFURCATION.NONLINEARITY. VOL. 16. ISSUE 1. P. 277-300 19 100% 21

Classes with closest relation at Level 1


Rank Class id link
1 22851 BIFURCATION CONTROL//CONTROL BIFURCATIONS//FEEDBACK CLASSIFICATION
2 15600 ORBIT FLIP//INCLINATION FLIP//T POINT
3 17410 HETEROCLINIC NETWORK//COUPLED CELL NETWORKS//HETEROCLINIC CYCLE
4 24086 UMR 8101//HAMILTONIAN MONODROMY//ENERGY MOMENTUM MAP
5 28113 GREENS RESIDUE//HAMILTONIAN NORMAL FORM//HIGH FREQUENCY VIBRATION OF SUSPENSION POINT
6 13858 SOMMERFELD EFFECT//NON IDEAL SYSTEM//ELECT ENGN MENOUF
7 2324 LIMIT CYCLE//ABELIAN INTEGRALS//ISOCHRONOUS CENTER
8 13113 HOLOMORPHIC FOLIATION//ANALYTIC CLASSIFICATION//LOTKA VOLTERRA DERIVATION
9 21166 FAST EXCITATION//GRP NONLINEAR OSCILLAT CHAOS//ASYMPTOTIC APPROXIMATION OF FIRST INTEGRAL
10 37569 COSYMMETRY//FAMILY OF EQUILIBRIA//FAMILIES OF EQUILIBRIA

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