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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] 110480

37-00

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

37-01

Instructional exposition (textbooks, tutorial papers, etc.) 457

37-02

Research exposition (monographs, survey articles) 1060

37-03

Historical (must also be assigned at least one classification number from Section 01) 240

37-04

Explicit machine computation and programs (not the theory of computation or programming) 161

37-06

Proceedings, conferences, collections, etc. 998

37Axx

Ergodic theory [See also 28Dxx] 10413

37A05

Measure-preserving transformations 1340

37A10

One-parameter continuous families of measure-preserving transformations 185

37A15

General groups of measure-preserving transformations [See mainly 22Fxx] 499

37A17

Homogeneous flows [See also 22Fxx] 189

37A20

Orbit equivalence, cocycles, ergodic equivalence relations 672

37A25

Ergodicity, mixing, rates of mixing 1764

37A30

Ergodic theorems, spectral theory, Markov operators [For operator ergodic theory, see mainly 47A35] 1540

37A35

Entropy and other invariants, isomorphism, classification 1310

37A40

Nonsingular (and infinite-measure preserving) transformations 258

37A45

Relations with number theory and harmonic analysis [See also 11Kxx] 947

37A50

Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 854

37A55

Relations with the theory of \(C^*\)-algebras [See mainly 46L55] 205

37A60

Dynamical systems in statistical mechanics [See also 82Cxx] 488

37A99

None of the above, but in this section 2195

37Bxx

Topological dynamics [See also 54H20] 10844

37B05

Transformations and group actions with special properties (minimality, distality, proximality, etc.) 1359

37B10

Symbolic dynamics [See also 37Cxx, 37Dxx] 2703

37B15

Cellular automata [See also 68Q80] 1299

37B20

Notions of recurrence 770

37B25

Lyapunov functions and stability; attractors, repellers 951

37B30

Index theory, Morse-Conley indices 512

37B35

Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets 223

37B40

Topological entropy 1666

37B45

Continua theory in dynamics 299

37B50

Multi-dimensional shifts of finite type, tiling dynamics 544

37B55

Nonautonomous dynamical systems 632

37B99

None of the above, but in this section 1843

37Cxx

Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx] 17841

37C05

Smooth mappings and diffeomorphisms 874

37C10

Vector fields, flows, ordinary differential equations 2828

37C15

Topological and differentiable equivalence, conjugacy, invariants, moduli, classification 877

37C20

Generic properties, structural stability 594

37C25

Fixed points, periodic points, fixed-point index theory 1840

37C27

Periodic orbits of vector fields and flows 752

37C29

Homoclinic and heteroclinic orbits 1091

37C30

Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems 884

37C35

Orbit growth 166

37C40

Smooth ergodic theory, invariant measures [See also 37Dxx] 988

37C45

Dimension theory of dynamical systems 910

37C50

Approximate trajectories (pseudotrajectories, shadowing, etc.) 545

37C55

Periodic and quasiperiodic flows and diffeomorphisms 463

37C60

Nonautonomous smooth dynamical systems [See also 37B55] 599

37C65

Monotone flows 118

37C70

Attractors and repellers, topological structure 2589

37C75

Stability theory 2469

37C80

Symmetries, equivariant dynamical systems 1077

37C85

Dynamics of group actions other than \(\mathbb Z\) and \(\mathbb R\), and foliations [See mainly 22Fxx, and also 57R30, 57Sxx] 1026

37C99

None of the above, but in this section 239

37Dxx

Dynamical systems with hyperbolic behavior 21051

37D05

Hyperbolic orbits and sets 483

37D10

Invariant manifold theory 690

37D15

Morse-Smale systems 620

37D20

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 1535

37D25

Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 1078

37D30

Partially hyperbolic systems and dominated splittings 628

37D35

Thermodynamic formalism, variational principles, equilibrium states 806

37D40

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 1756

37D45

Strange attractors, chaotic dynamics 12607

37D50

Hyperbolic systems with singularities (billiards, etc.) 943

37D99

None of the above, but in this section 1776

37Exx

Low-dimensional dynamical systems 6642

37E05

Maps of the interval (piecewise continuous, continuous, smooth) 2308

37E10

Maps of the circle 789

37E15

Combinatorial dynamics (types of periodic orbits) 349

37E20

Universality, renormalization [See also 37F25] 304

37E25

Maps of trees and graphs 369

37E30

Homeomorphisms and diffeomorphisms of planes and surfaces 1069

37E35

Flows on surfaces 370

37E40

Twist maps 268

37E45

Rotation numbers and vectors 452

37E99

None of the above, but in this section 1339

37Fxx

Complex dynamical systems [See also 30D05, 32H50] 4811

37F05

Relations and correspondences 52

37F10

Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 2170

37F15

Expanding maps; hyperbolicity; structural stability 246

37F20

Combinatorics and topology 287

37F25

Renormalization 178

37F30

Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems 367

37F35

Conformal densities and Hausdorff dimension 427

37F40

Geometric limits 40

37F45

Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations 663

37F50

Small divisors, rotation domains and linearization; Fatou and Julia sets 1149

37F75

Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx] 536

37F99

None of the above, but in this section 513

37Gxx

Local and nonlocal bifurcation theory [See also 34C23, 34K18] 8286

37G05

Normal forms 786

37G10

Bifurcations of singular points 874

37G15

Bifurcations of limit cycles and periodic orbits 2138

37G20

Hyperbolic singular points with homoclinic trajectories 290

37G25

Bifurcations connected with nontransversal intersection 209

37G30

Infinite nonwandering sets arising in bifurcations 34

37G35

Attractors and their bifurcations 475

37G40

Symmetries, equivariant bifurcation theory 540

37G99

None of the above, but in this section 3693

37Hxx

Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx] 2073

37H05

Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx] 145

37H10

Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15] 1073

37H15

Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx] 402

37H20

Bifurcation theory [See also 37Gxx] 147

37H99

None of the above, but in this section 403

37Jxx

Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx] 17370

37J05

General theory, relations with symplectic geometry and topology 1267

37J10

Symplectic mappings, fixed points 643

37J15

Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20] 1040

37J20

Bifurcation problems 378

37J25

Stability problems 471

37J30

Obstructions to integrability (nonintegrability criteria) 306

37J35

Completely integrable systems, topological structure of phase space, integration methods 5125

37J40

Perturbations, normal forms, small divisors, KAM theory, Arnol’d diffusion 2148

37J45

Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods 1716

37J50

Action-minimizing orbits and measures 334

37J55

Contact systems [See also 53D10] 103

37J60

Nonholonomic dynamical systems [See also 70F25] 414

37J99

None of the above, but in this section 5695

37Kxx

Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] 17326

37K05

Hamiltonian structures, symmetries, variational principles, conservation laws 1628

37K10

Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 9993

37K15

Integration of completely integrable systems by inverse spectral and scattering methods 1082

37K20

Relations with algebraic geometry, complex analysis, special functions [See also 14H70] 801

37K25

Relations with differential geometry 642

37K30

Relations with infinite-dimensional Lie algebras and other algebraic structures 935

37K35

Lie-Bäcklund and other transformations 1832

37K40

Soliton theory, asymptotic behavior of solutions 2639

37K45

Stability problems 457

37K50

Bifurcation problems 235

37K55

Perturbations, KAM for infinite-dimensional systems 415

37K60

Lattice dynamics [See also 37L60] 1281

37K65

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

37K99

None of the above, but in this section 85

37Lxx

Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx] 3853

37L05

General theory, nonlinear semigroups, evolution equations 488

37L10

Normal forms, center manifold theory, bifurcation theory 381

37L15

Stability problems 323

37L20

Symmetries 93

37L25

Inertial manifolds and other invariant attracting sets 255

37L30

Attractors and their dimensions, Lyapunov exponents 1370

37L40

Invariant measures 157

37L45

Hyperbolicity; Lyapunov functions 78

37L50

Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems 123

37L55

Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] 343

37L60

Lattice dynamics [See also 37K60] 477

37L65

Special approximation methods (nonlinear Galerkin, etc.) 121

37L99

None of the above, but in this section 141

37Mxx

Approximation methods and numerical treatment of dynamical systems [See also 65Pxx] 4598

37M05

Simulation 985

37M10

Time series analysis 1172

37M15

Symplectic integrators 982

37M20

Computational methods for bifurcation problems 524

37M25

Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy) 582

37M99

None of the above, but in this section 448

37Nxx

Applications 17341

37N05

Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx] 1535

37N10

Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10] 1925

37N15

Dynamical systems in solid mechanics [See mainly 74Hxx] 487

37N20

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 2588

37N25

Dynamical systems in biology [See mainly 92-XX, but also 91-XX] 5602

37N30

Dynamical systems in numerical analysis 165

37N35

Dynamical systems in control 2129

37N40

Dynamical systems in optimization and economics 1275

37N99

None of the above, but in this section 1925

37Pxx

Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45] 600

37P05

Polynomial and rational maps 232

37P10

Analytic and meromorphic maps 15

37P15

Global ground fields 66

37P20

Non-Archimedean local ground fields 127

37P25

Finite ground fields 54

37P30

Height functions; Green functions; invariant measures [See also 11G50, 14G40] 102

37P35

Arithmetic properties of periodic points 76

37P40

Non-Archimedean Fatou and Julia sets 24

37P45

Families and moduli spaces 43

37P50

Dynamical systems on Berkovich spaces 41

37P55

Arithmetic dynamics on general algebraic varieties 81

37P99

None of the above, but in this section 17

Overview

General mathematics

History and biography

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Combinatorics

Order, lattices, ordered algebraic structures

General algebraic systems

Number theory

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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

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Difference and functional equations

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Approximation and expansions

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Mathematics Subject Classification – MSC2010

Overview