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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] 107228

37-00

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

37-01

Instructional exposition (textbooks, tutorial papers, etc.) 445

37-02

Research exposition (monographs, survey articles) 1040

37-03

Historical (must also be assigned at least one classification number from Section 01) 228

37-04

Explicit machine computation and programs (not the theory of computation or programming) 158

37-06

Proceedings, conferences, collections, etc. 976

37Axx

Ergodic theory [See also 28Dxx] 10061

37A05

Measure-preserving transformations 1298

37A10

One-parameter continuous families of measure-preserving transformations 177

37A15

General groups of measure-preserving transformations [See mainly 22Fxx] 487

37A17

Homogeneous flows [See also 22Fxx] 171

37A20

Orbit equivalence, cocycles, ergodic equivalence relations 652

37A25

Ergodicity, mixing, rates of mixing 1688

37A30

Ergodic theorems, spectral theory, Markov operators [For operator ergodic theory, see mainly 47A35] 1483

37A35

Entropy and other invariants, isomorphism, classification 1245

37A40

Nonsingular (and infinite-measure preserving) transformations 238

37A45

Relations with number theory and harmonic analysis [See also 11Kxx] 889

37A50

Relations with probability theory and stochastic processes [See also 60Fxx and 60G10] 822

37A55

Relations with the theory of $C^*$-algebras [See mainly 46L55] 191

37A60

Dynamical systems in statistical mechanics [See also 82Cxx] 473

37A99

None of the above, but in this section 2190

37Bxx

Topological dynamics [See also 54H20] 10482

37B05

Transformations and group actions with special properties (minimality, distality, proximality, etc.) 1288

37B10

Symbolic dynamics [See also 37Cxx, 37Dxx] 2609

37B15

Cellular automata [See also 68Q80] 1251

37B20

Notions of recurrence 731

37B25

Lyapunov functions and stability; attractors, repellers 924

37B30

Index theory, Morse-Conley indices 504

37B35

Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets 211

37B40

Topological entropy 1583

37B45

Continua theory in dynamics 286

37B50

Multi-dimensional shifts of finite type, tiling dynamics 502

37B55

Nonautonomous dynamical systems 596

37B99

None of the above, but in this section 1835

37Cxx

Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx] 17412

37C05

Smooth mappings and diffeomorphisms 840

37C10

Vector fields, flows, ordinary differential equations 2765

37C15

Topological and differentiable equivalence, conjugacy, invariants, moduli, classification 846

37C20

Generic properties, structural stability 575

37C25

Fixed points, periodic points, fixed-point index theory 1802

37C27

Periodic orbits of vector fields and flows 738

37C29

Homoclinic and heteroclinic orbits 1058

37C30

Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems 849

37C35

Orbit growth 161

37C40

Smooth ergodic theory, invariant measures [See also 37Dxx] 956

37C45

Dimension theory of dynamical systems 890

37C50

Approximate trajectories (pseudotrajectories, shadowing, etc.) 519

37C55

Periodic and quasiperiodic flows and diffeomorphisms 450

37C60

Nonautonomous smooth dynamical systems [See also 37B55] 565

37C65

Monotone flows 109

37C70

Attractors and repellers, topological structure 2558

37C75

Stability theory 2427

37C80

Symmetries, equivariant dynamical systems 1069

37C85

Dynamics of group actions other than $\Bbb Z$ and $\Bbb R$, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx] 994

37C99

None of the above, but in this section 237

37Dxx

Dynamical systems with hyperbolic behavior 20554

37D05

Hyperbolic orbits and sets 470

37D10

Invariant manifold theory 666

37D15

Morse-Smale systems 612

37D20

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 1496

37D25

Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 1037

37D30

Partially hyperbolic systems and dominated splittings 604

37D35

Thermodynamic formalism, variational principles, equilibrium states 761

37D40

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 1687

37D45

Strange attractors, chaotic dynamics 12353

37D50

Hyperbolic systems with singularities (billiards, etc.) 899

37D99

None of the above, but in this section 1775

37Exx

Low-dimensional dynamical systems 6432

37E05

Maps of the interval (piecewise continuous, continuous, smooth) 2240

37E10

Maps of the circle 739

37E15

Combinatorial dynamics (types of periodic orbits) 335

37E20

Universality, renormalization [See also 37F25] 298

37E25

Maps of trees and graphs 351

37E30

Homeomorphisms and diffeomorphisms of planes and surfaces 1029

37E35

Flows on surfaces 355

37E40

Twist maps 262

37E45

Rotation numbers and vectors 427

37E99

None of the above, but in this section 1332

37Fxx

Complex dynamical systems [See also 30D05, 32H50] 4687

37F05

Relations and correspondences 49

37F10

Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04] 2114

37F15

Expanding maps; hyperbolicity; structural stability 245

37F20

Combinatorics and topology 276

37F25

Renormalization 170

37F30

Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems 356

37F35

Conformal densities and Hausdorff dimension 422

37F40

Geometric limits 38

37F45

Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations 634

37F50

Small divisors, rotation domains and linearization; Fatou and Julia sets 1132

37F75

Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx] 511

37F99

None of the above, but in this section 506

37Gxx

Local and nonlocal bifurcation theory [See also 34C23, 34K18] 8161

37G05

Normal forms 772

37G10

Bifurcations of singular points 840

37G15

Bifurcations of limit cycles and periodic orbits 2092

37G20

Hyperbolic singular points with homoclinic trajectories 284

37G25

Bifurcations connected with nontransversal intersection 206

37G30

Infinite nonwandering sets arising in bifurcations 34

37G35

Attractors and their bifurcations 459

37G40

Symmetries, equivariant bifurcation theory 531

37G99

None of the above, but in this section 3685

37Hxx

Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx] 1966

37H05

Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx] 140

37H10

Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15] 1006

37H15

Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx] 375

37H20

Bifurcation theory [See also 37Gxx] 143

37H99

None of the above, but in this section 402

37Jxx

Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx] 17070

37J05

General theory, relations with symplectic geometry and topology 1232

37J10

Symplectic mappings, fixed points 625

37J15

Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20] 1015

37J20

Bifurcation problems 360

37J25

Stability problems 453

37J30

Obstructions to integrability (nonintegrability criteria) 294

37J35

Completely integrable systems, topological structure of phase space, integration methods 5038

37J40

Perturbations, normal forms, small divisors, KAM theory, Arnol’d diffusion 2104

37J45

Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods 1649

37J50

Action-minimizing orbits and measures 324

37J55

Contact systems [See also 53D10] 93

37J60

Nonholonomic dynamical systems [See also 70F25] 393

37J99

None of the above, but in this section 5689

37Kxx

Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx] 16882

37K05

Hamiltonian structures, symmetries, variational principles, conservation laws 1576

37K10

Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 9736

37K15

Integration of completely integrable systems by inverse spectral and scattering methods 1046

37K20

Relations with algebraic geometry, complex analysis, special functions [See also 14H70] 773

37K25

Relations with differential geometry 614

37K30

Relations with infinite-dimensional Lie algebras and other algebraic structures 900

37K35

Lie-Bäcklund and other transformations 1765

37K40

Soliton theory, asymptotic behavior of solutions 2578

37K45

Stability problems 450

37K50

Bifurcation problems 226

37K55

Perturbations, KAM for infinite-dimensional systems 395

37K60

Lattice dynamics [See also 37L60] 1259

37K65

Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics 187

37K99

None of the above, but in this section 84

37Lxx

Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx] 3720

37L05

General theory, nonlinear semigroups, evolution equations 473

37L10

Normal forms, center manifold theory, bifurcation theory 361

37L15

Stability problems 310

37L20

Symmetries 88

37L25

Inertial manifolds and other invariant attracting sets 251

37L30

Attractors and their dimensions, Lyapunov exponents 1329

37L40

Invariant measures 152

37L45

Hyperbolicity; Lyapunov functions 73

37L50

Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems 120

37L55

Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] 311

37L60

Lattice dynamics [See also 37K60] 468

37L65

Special approximation methods (nonlinear Galerkin, etc.) 113

37L99

None of the above, but in this section 141

37Mxx

Approximation methods and numerical treatment of dynamical systems [See also 65Pxx] 4469

37M05

Simulation 953

37M10

Time series analysis 1140

37M15

Symplectic integrators 966

37M20

Computational methods for bifurcation problems 513

37M25

Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy) 560

37M99

None of the above, but in this section 434

37Nxx

Applications 16896

37N05

Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx] 1477

37N10

Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10] 1872

37N15

Dynamical systems in solid mechanics [See mainly 74Hxx] 468

37N20

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 2549

37N25

Dynamical systems in biology [See mainly 92-XX, but also 91-XX] 5450

37N30

Dynamical systems in numerical analysis 155

37N35

Dynamical systems in control 2079

37N40

Dynamical systems in optimization and economics 1224

37N99

None of the above, but in this section 1918

37Pxx

Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45] 543

37P05

Polynomial and rational maps 205

37P10

Analytic and meromorphic maps 14

37P15

Global ground fields 61

37P20

Non-Archimedean local ground fields 122

37P25

Finite ground fields 47

37P30

Height functions; Green functions; invariant measures [See also 11G50, 14G40] 91

37P35

Arithmetic properties of periodic points 69

37P40

Non-Archimedean Fatou and Julia sets 23

37P45

Families and moduli spaces 37

37P50

Dynamical systems on Berkovich spaces 37

37P55

Arithmetic dynamics on general algebraic varieties 69

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

Calculus of variations and optimal control; optimization

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General topology

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Systems theory; control

Information and communication, circuits

Mathematics education

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Mathematics Subject Classification – MSC2010

Overview