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Mathematics Subject Classification – MSC2010

37-XX

Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] 109262

37-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 12

37-01

Instructional exposition (textbooks, tutorial papers, etc.) 450

37-02

Research exposition (monographs, survey articles) 1051

37-03

Historical (must also be assigned at least one classification number from Section 01) 239

37-04

Explicit machine computation and programs (not the theory of computation or programming) 160

37-06

Proceedings, conferences, collections, etc. 990

37Axx

Ergodic theory [See also 28Dxx] 10302

37A05

Measure-preserving transformations 1327

37A10

One-parameter continuous families of measure-preserving transformations 182

37A15

General groups of measure-preserving transformations [See mainly 22Fxx] 495

37A17

Homogeneous flows [See also 22Fxx] 188

37A20

Orbit equivalence, cocycles, ergodic equivalence relations 667

37A25

Ergodicity, mixing, rates of mixing 1735

37A30

Ergodic theorems, spectral theory, Markov operators [For operator ergodic theory, see mainly 47A35] 1517

37A35

Entropy and other invariants, isomorphism, classification 1292

37A40

Nonsingular (and infinite-measure preserving) transformations 249

37A45

Relations with number theory and harmonic analysis [See also 11Kxx] 934

37A50

Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 842

37A55

Relations with the theory of $C^*$-algebras [See mainly 46L55] 198

37A60

Dynamical systems in statistical mechanics [See also 82Cxx] 485

37A99

None of the above, but in this section 2194

37Bxx

Topological dynamics [See also 54H20] 10736

37B05

Transformations and group actions with special properties (minimality, distality, proximality, etc.) 1336

37B10

Symbolic dynamics [See also 37Cxx, 37Dxx] 2674

37B15

Cellular automata [See also 68Q80] 1289

37B20

Notions of recurrence 755

37B25

Lyapunov functions and stability; attractors, repellers 935

37B30

Index theory, Morse-Conley indices 508

37B35

Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets 219

37B40

Topological entropy 1634

37B45

Continua theory in dynamics 293

37B50

Multi-dimensional shifts of finite type, tiling dynamics 524

37B55

Nonautonomous dynamical systems 618

37B99

None of the above, but in this section 1844

37Cxx

Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx] 17685

37C05

Smooth mappings and diffeomorphisms 863

37C10

Vector fields, flows, ordinary differential equations 2803

37C15

Topological and differentiable equivalence, conjugacy, invariants, moduli, classification 860

37C20

Generic properties, structural stability 581

37C25

Fixed points, periodic points, fixed-point index theory 1823

37C27

Periodic orbits of vector fields and flows 746

37C29

Homoclinic and heteroclinic orbits 1077

37C30

Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems 873

37C35

Orbit growth 163

37C40

Smooth ergodic theory, invariant measures [See also 37Dxx] 974

37C45

Dimension theory of dynamical systems 900

37C50

Approximate trajectories (pseudotrajectories, shadowing, etc.) 537

37C55

Periodic and quasiperiodic flows and diffeomorphisms 459

37C60

Nonautonomous smooth dynamical systems [See also 37B55] 591

37C65

Monotone flows 115

37C70

Attractors and repellers, topological structure 2579

37C75

Stability theory 2450

37C80

Symmetries, equivariant dynamical systems 1072

37C85

Dynamics of group actions other than $\Bbb Z$ and $\Bbb R$, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx] 1022

37C99

None of the above, but in this section 240

37Dxx

Dynamical systems with hyperbolic behavior 20886

37D05

Hyperbolic orbits and sets 480

37D10

Invariant manifold theory 682

37D15

Morse-Smale systems 616

37D20

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 1521

37D25

Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 1064

37D30

Partially hyperbolic systems and dominated splittings 625

37D35

Thermodynamic formalism, variational principles, equilibrium states 791

37D40

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 1733

37D45

Strange attractors, chaotic dynamics 12515

37D50

Hyperbolic systems with singularities (billiards, etc.) 931

37D99

None of the above, but in this section 1774

37Exx

Low-dimensional dynamical systems 6570

37E05

Maps of the interval (piecewise continuous, continuous, smooth) 2289

37E10

Maps of the circle 775

37E15

Combinatorial dynamics (types of periodic orbits) 343

37E20

Universality, renormalization [See also 37F25] 305

37E25

Maps of trees and graphs 361

37E30

Homeomorphisms and diffeomorphisms of planes and surfaces 1051

37E35

Flows on surfaces 364

37E40

Twist maps 266

37E45

Rotation numbers and vectors 446

37E99

None of the above, but in this section 1336

37Fxx

Complex dynamical systems [See also 30D05, 32H50] 4769

37F05

Relations and correspondences 51

37F10

Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 2148

37F15

Expanding maps; hyperbolicity; structural stability 244

37F20

Combinatorics and topology 284

37F25

Renormalization 177

37F30

Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems 365

37F35

Conformal densities and Hausdorff dimension 427

37F40

Geometric limits 41

37F45

Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations 657

37F50

Small divisors, rotation domains and linearization; Fatou and Julia sets 1144

37F75

Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx] 525

37F99

None of the above, but in this section 512

37Gxx

Local and nonlocal bifurcation theory [See also 34C23, 34K18] 8238

37G05

Normal forms 776

37G10

Bifurcations of singular points 860

37G15

Bifurcations of limit cycles and periodic orbits 2121

37G20

Hyperbolic singular points with homoclinic trajectories 291

37G25

Bifurcations connected with nontransversal intersection 209

37G30

Infinite nonwandering sets arising in bifurcations 34

37G35

Attractors and their bifurcations 471

37G40

Symmetries, equivariant bifurcation theory 537

37G99

None of the above, but in this section 3690

37Hxx

Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx] 2032

37H05

Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx] 143

37H10

Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15] 1046

37H15

Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx] 391

37H20

Bifurcation theory [See also 37Gxx] 146

37H99

None of the above, but in this section 404

37Jxx

Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx] 17263

37J05

General theory, relations with symplectic geometry and topology 1252

37J10

Symplectic mappings, fixed points 637

37J15

Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20] 1030

37J20

Bifurcation problems 370

37J25

Stability problems 462

37J30

Obstructions to integrability (nonintegrability criteria) 300

37J35

Completely integrable systems, topological structure of phase space, integration methods 5098

37J40

Perturbations, normal forms, small divisors, KAM theory, Arnol’d diffusion 2137

37J45

Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods 1692

37J50

Action-minimizing orbits and measures 332

37J55

Contact systems [See also 53D10] 98

37J60

Nonholonomic dynamical systems [See also 70F25] 407

37J99

None of the above, but in this section 5692

37Kxx

Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] 17194

37K05

Hamiltonian structures, symmetries, variational principles, conservation laws 1615

37K10

Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 9918

37K15

Integration of completely integrable systems by inverse spectral and scattering methods 1067

37K20

Relations with algebraic geometry, complex analysis, special functions [See also 14H70] 792

37K25

Relations with differential geometry 634

37K30

Relations with infinite-dimensional Lie algebras and other algebraic structures 925

37K35

Lie-Bäcklund and other transformations 1807

37K40

Soliton theory, asymptotic behavior of solutions 2620

37K45

Stability problems 454

37K50

Bifurcation problems 228

37K55

Perturbations, KAM for infinite-dimensional systems 412

37K60

Lattice dynamics [See also 37L60] 1275

37K65

Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics 189

37K99

None of the above, but in this section 84

37Lxx

Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx] 3817

37L05

General theory, nonlinear semigroups, evolution equations 484

37L10

Normal forms, center manifold theory, bifurcation theory 377

37L15

Stability problems 322

37L20

Symmetries 88

37L25

Inertial manifolds and other invariant attracting sets 254

37L30

Attractors and their dimensions, Lyapunov exponents 1357

37L40

Invariant measures 156

37L45

Hyperbolicity; Lyapunov functions 77

37L50

Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems 122

37L55

Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] 336

37L60

Lattice dynamics [See also 37K60] 474

37L65

Special approximation methods (nonlinear Galerkin, etc.) 117

37L99

None of the above, but in this section 141

37Mxx

Approximation methods and numerical treatment of dynamical systems [See also 65Pxx] 4569

37M05

Simulation 981

37M10

Time series analysis 1164

37M15

Symplectic integrators 976

37M20

Computational methods for bifurcation problems 524

37M25

Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy) 579

37M99

None of the above, but in this section 446

37Nxx

Applications 17197

37N05

Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx] 1517

37N10

Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10] 1913

37N15

Dynamical systems in solid mechanics [See mainly 74Hxx] 483

37N20

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 2577

37N25

Dynamical systems in biology [See mainly 92-XX, but also 91-XX] 5541

37N30

Dynamical systems in numerical analysis 162

37N35

Dynamical systems in control 2113

37N40

Dynamical systems in optimization and economics 1259

37N99

None of the above, but in this section 1923

37Pxx

Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45] 582

37P05

Polynomial and rational maps 225

37P10

Analytic and meromorphic maps 14

37P15

Global ground fields 65

37P20

Non-Archimedean local ground fields 125

37P25

Finite ground fields 50

37P30

Height functions; Green functions; invariant measures [See also 11G50, 14G40] 99

37P35

Arithmetic properties of periodic points 75

37P40

Non-Archimedean Fatou and Julia sets 23

37P45

Families and moduli spaces 41

37P50

Dynamical systems on Berkovich spaces 39

37P55

Arithmetic dynamics on general algebraic varieties 81

37P99

None of the above, but in this section 15

Overview

General mathematics

History and biography

Mathematical logic and foundations

Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

Field theory and polynomials

Commutative algebra

Algebraic geometry

Linear and multilinear algebra; matrix theory

Associative rings and algebras

Nonassociative rings and algebras

Category theory, homological algebra

$K$-theory

Group theory and generalizations

Topological groups, Lie groups

Real functions

Measure and integration

Functions of a complex variable

Potential theory

Several complex variables and analytic spaces

Special functions

Ordinary differential equations

Partial differential equations

Dynamical systems and ergodic theory

Difference and functional equations

Sequences, series, summability

Approximation and expansions

Harmonic analysis on Euclidean spaces

Abstract harmonic analysis

Integral transforms, operational calculus

Integral equations

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Operator theory

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Differential geometry

General topology

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Manifolds and cell complexes

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Systems theory; control

Information and communication, circuits

Mathematics education

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Mathematics Subject Classification – MSC2010

Overview