Class information for:
Level 1: KAM THEORY//ARNOLD DIFFUSION//KAM ITERATION

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
9161 1182 24.9 44%


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
197 3       CHAOS//INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS//PHYSICS, MATHEMATICAL 53660
386 2             ERGODIC THEORY AND DYNAMICAL SYSTEMS//NONLINEARITY//TOPOLOGICAL ENTROPY 16977
9161 1                   KAM THEORY//ARNOLD DIFFUSION//KAM ITERATION 1182

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 KAM THEORY authKW 1194675 8% 50% 92
2 ARNOLD DIFFUSION authKW 804122 3% 76% 41
3 KAM ITERATION authKW 777996 3% 94% 32
4 QUASI PERIODIC SOLUTIONS authKW 529797 5% 35% 58
5 NEKHOROSHEV THEOREM authKW 488033 2% 82% 23
6 INVARIANT TORI authKW 432235 4% 36% 47
7 SPLITTING OF SEPARATRICES authKW 388998 1% 94% 16
8 INFINITE DIMENSIONAL HAMILTONIAN SYSTEMS authKW 321551 2% 66% 19
9 NON DEGENERACY CONDITION authKW 297823 1% 82% 14
10 SMALL DIVISORS authKW 272888 2% 39% 27

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 19467 51% 0% 600
2 Physics, Mathematical 15440 32% 0% 379
3 Mathematics 14860 48% 0% 573
4 Mechanics 472 8% 0% 93
5 Mathematics, Interdisciplinary Applications 441 5% 0% 57
6 Physics, Multidisciplinary 295 9% 0% 105
7 Astronomy & Astrophysics 127 6% 0% 68
8 Physics, Fluids & Plasmas 0 1% 0% 8
9 History & Philosophy of Science -0 0% 0% 1
10 Humanities, Multidisciplinary -0 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 OBSERV NICE 80721 0% 63% 5
2 MATH J LERAY 78716 1% 38% 8
3 MATEMAT LICADA ANAL 76148 3% 8% 37
4 ANAL GEOMETRIE PLICATUMR 7539 64575 0% 50% 5
5 MATEMAT LICADA 1 63843 4% 5% 46
6 ETSEIB MATEMAT LICADA 51664 0% 100% 2
7 DIPARTIMENTO MATEMAT PLICAZ R CACCIOPPOLI 43129 2% 6% 28
8 GEOMETR ANAL GRP 34441 0% 67% 2
9 MECAN CELESTE 33209 0% 43% 3
10 UMR CNRS 6629 29425 1% 16% 7

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 87954 4% 7% 48
2 NONLINEARITY 43474 6% 2% 74
3 CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY 27529 4% 2% 44
4 JOURNAL OF DIFFERENTIAL EQUATIONS 24060 7% 1% 82
5 DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 20893 4% 2% 52
6 ERGODIC THEORY AND DYNAMICAL SYSTEMS 14675 3% 2% 37
7 COMMUNICATIONS IN MATHEMATICAL PHYSICS 14614 6% 1% 68
8 JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS 11402 1% 3% 14
9 QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 9576 1% 5% 7
10 PHYSICA D-NONLINEAR PHENOMENA 8932 4% 1% 47

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 KAM THEORY 1194675 8% 50% 92 Search KAM+THEORY Search KAM+THEORY
2 ARNOLD DIFFUSION 804122 3% 76% 41 Search ARNOLD+DIFFUSION Search ARNOLD+DIFFUSION
3 KAM ITERATION 777996 3% 94% 32 Search KAM+ITERATION Search KAM+ITERATION
4 QUASI PERIODIC SOLUTIONS 529797 5% 35% 58 Search QUASI+PERIODIC+SOLUTIONS Search QUASI+PERIODIC+SOLUTIONS
5 NEKHOROSHEV THEOREM 488033 2% 82% 23 Search NEKHOROSHEV+THEOREM Search NEKHOROSHEV+THEOREM
6 INVARIANT TORI 432235 4% 36% 47 Search INVARIANT+TORI Search INVARIANT+TORI
7 SPLITTING OF SEPARATRICES 388998 1% 94% 16 Search SPLITTING+OF+SEPARATRICES Search SPLITTING+OF+SEPARATRICES
8 INFINITE DIMENSIONAL HAMILTONIAN SYSTEMS 321551 2% 66% 19 Search INFINITE+DIMENSIONAL+HAMILTONIAN+SYSTEMS Search INFINITE+DIMENSIONAL+HAMILTONIAN+SYSTEMS
9 NON DEGENERACY CONDITION 297823 1% 82% 14 Search NON+DEGENERACY+CONDITION Search NON+DEGENERACY+CONDITION
10 SMALL DIVISORS 272888 2% 39% 27 Search SMALL+DIVISORS Search SMALL+DIVISORS

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 LIU, J , SI, JG , (2017) INVARIANT TORT OF A NONLINEAR SCHRODINGER EQUATION WITH QUASI-PERIODICALLY UNBOUNDED PERTURBATIONS.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. VOL. 16. ISSUE 1. P. 25 -68 31 100% 0
2 GUZZO, M , (2015) THE NEKHOROSHEV THEOREM AND LONG-TERM STABILITIES IN THE SOLAR SYSTEM.SERBIAN ASTRONOMICAL JOURNAL. VOL. 190. ISSUE . P. 1 -10 43 73% 1
3 SEVRYUK, MB , (2003) THE CLASSICAL KAM THEORY AT THE DAWN OF THE TWENTY-FIRST CENTURY.MOSCOW MATHEMATICAL JOURNAL. VOL. 3. ISSUE 3. P. 1113 -1144 47 87% 19
4 GUARDIA, M , HAUS, E , PROCESI, M , (2016) GROWTH OF SOBOLEV NORMS FOR THE ANALYTIC NLS ON T-2.ADVANCES IN MATHEMATICS. VOL. 301. ISSUE . P. 615 -692 35 83% 0
5 BALDOMA, I , FONTICH, E , GUARDIA, M , SEARA, TM , (2012) EXPONENTIALLY SMALL SPLITTING OF SEPARATRICES BEYOND MELNIKOV ANALYSIS: RIGOROUS RESULTS.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 253. ISSUE 12. P. 3304 -3439 32 94% 8
6 GUZZO, M , CHIERCHIA, L , BENETTIN, G , (2016) THE STEEP NEKHOROSHEV'S THEOREM.COMMUNICATIONS IN MATHEMATICAL PHYSICS. VOL. 342. ISSUE 2. P. 569 -601 23 96% 4
7 SEVRYUK, MB , (2006) PARTIAL PRESERVATION OF FREQUENCIES IN KAM THEORY.NONLINEARITY. VOL. 19. ISSUE 5. P. 1099-1140 40 87% 23
8 GUARDIA, M , SEARA, TM , (2012) EXPONENTIALLY AND NON-EXPONENTIALLY SMALL SPLITTING OF SEPARATRICES FOR THE PENDULUM WITH A FAST MEROMORPHIC PERTURBATION.NONLINEARITY. VOL. 25. ISSUE 5. P. 1367-1412 31 94% 6
9 GUZZO, M , LEGA, E , (2016) THE NEKHOROSHEV THEOREM AND THE OBSERVATION OF LONG-TERM DIFFUSION IN HAMILTONIAN SYSTEMS.REGULAR & CHAOTIC DYNAMICS. VOL. 21. ISSUE 6. P. 707 -719 30 88% 0
10 REN, XF , (2014) QUASI-PERIODIC SOLUTIONS WITH PRESCRIBED FREQUENCY IN REVERSIBLE SYSTEMS.JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS. VOL. 26. ISSUE 3. P. 493 -515 28 97% 1

Classes with closest relation at Level 1


Rank Class id link
1 8275 CIRCLE HOMEOMORPHISM//ROTATION NUMBER//CRITICAL CIRCLE MAPS
2 14490 WEAK KAM THEORY//AUBRY MATHER THEORY//HAMILTON JACOBI EQUATION
3 19076 NONLINEAR SUPRATRANSMISSION//SUPRATRANSMISSION//NONLINEAR BISTABILITY
4 24086 UMR 8101//HAMILTONIAN MONODROMY//ENERGY MOMENTUM MAP
5 12016 CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY//KIRKWOOD GAPS//CELESTIAL MECHANICS
6 18169 STRANGE NONCHAOTIC ATTRACTORS//QUASIPERIODICALLY FORCED SYSTEMS//ARNOLD RESONANCE WEB
7 28972 GFTC//THEORY CONTROL//FIS GERENCIA INVEST LICAC
8 19703 NORMAL FORM//UNIQUE NORMAL FORM//FURTHER REDUCTION
9 14916 CONLEY INDEX//RIGOROUS NUMERICS//COMPUTER ASSISTED PROOF
10 28113 GREENS RESIDUE//HAMILTONIAN NORMAL FORM//HIGH FREQUENCY VIBRATION OF SUSPENSION POINT

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