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Mathematics Subject Classification – MSC2020

History of dynamical systems and ergodic theory [Consider also classification numbers pertaining to Section 01-XX] 249

37-04

Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory 162

37-06

Proceedings, conferences, collections, etc. pertaining to dynamical systems and ergodic theory 1041

37-11

Research data for problems pertaining to dynamical systems and ergodic theory 0

37Axx

Ergodic theory [See also 28Dxx] 10956

37A05

Dynamical aspects of measure-preserving transformations 1411

37A10

Dynamical systems involving one-parameter continuous families of measure-preserving transformations 191

37A15

General groups of measure-preserving transformations and dynamical systems [See mainly 22Fxx] 546

37A17

Homogeneous flows [See also 22Fxx] 226

37A20

Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations 719

37A25

Ergodicity, mixing, rates of mixing 1870

37A30

Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35} 1661

37A35

Entropy and other invariants, isomorphism, classification in ergodic theory 1396

37A40

Nonsingular (and infinite-measure preserving) transformations 273

37A44

Relations between ergodic theory and number theory [See also 11Kxx] 32

37A46

Relations between ergodic theory and harmonic analysis 7

37A50

Dynamical systems and their relations with probability theory and stochastic processes [See also 60Fxx, 60G10] 917

37A55

Dynamical systems and the theory of \(C^*\)-algebras [See mainly 46L55] 227

37A60

Dynamical aspects of statistical mechanics [See also 82Cxx] 513

37A99

None of the above, but in this section 2197

37Bxx

Topological dynamics 11532

37B02

Dynamics in general topological spaces 53

37B05

Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 1501

37B10

Symbolic dynamics 2895

37B15

Dynamical aspects of cellular automata {For computational aspects, see 68Q80} 1369

37B20

Notions of recurrence and recurrent behavior in dynamical systems 827

37B25

Stability of topological dynamical systems 1012

37B30

Index theory for dynamical systems, Morse-Conley indices 540

37B35

Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets; attractors, repellers for topological dynamical systems 245

37B40

Topological entropy 1813

37B45

Continua theory in dynamics 323

37B51

Multidimensional shifts of finite type 39

37B52

Tiling dynamics 8

37B55

Topological dynamics of nonautonomous systems 707

37B65

Approximate trajectories, pseudotrajectories, shadowing and related notions for topological dynamical systems 18

37B99

None of the above, but in this section 1851

37Cxx

Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx] 18880

37C05

Dynamical systems involving smooth mappings and diffeomorphisms 972

37C10

Dynamics induced by flows and semiflows 2934

37C15

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 951

37C20

Generic properties, structural stability of dynamical systems 632

37C25

Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics 1958

37C27

Periodic orbits of vector fields and flows 819

37C29

Homoclinic and heteroclinic orbits for dynamical systems 1152

37C30

Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 936

37C35

Orbit growth in dynamical systems 201

37C40

Smooth ergodic theory, invariant measures for smooth dynamical systems [See also 37Dxx] 1076

37C45

Dimension theory of smooth dynamical systems 965

37C50

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics 593

37C55

Periodic and quasi-periodic flows and diffeomorphisms 494

37C60

Nonautonomous smooth dynamical systems [See also 37B55] 714

37C65

Monotone flows as dynamical systems 134

37C70

Attractors and repellers of smooth dynamical systems and their topological structure 2672

37C75

Stability theory for smooth dynamical systems 2574

37C79

Symmetries and invariants of dynamical systems [See also 34C14, 34K04] 11

37C81

Equivariant dynamical systems 0

37C83

Dynamical systems with singularities (billiards, etc.) 40

37C85

Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) [See mainly 22Fxx, and also 32M25, 57R30, 57Sxx] 1119

37C86

Foliations generated by dynamical systems 17

37C99

None of the above, but in this section 240

37Dxx

Dynamical systems with hyperbolic behavior 21863

37D05

Dynamical systems with hyperbolic orbits and sets 507

37D10

Invariant manifold theory for dynamical systems 721

37D15

Morse-Smale systems 644

37D20

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 1605

37D25

Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 1151

37D30

Partially hyperbolic systems and dominated splittings 679

37D35

Thermodynamic formalism, variational principles, equilibrium states for dynamical systems 900

37D40

Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 1842

37D45

Strange attractors, chaotic dynamics of systems with hyperbolic behavior 13025

37D99

None of the above, but in this section 1781

37Exx

Low-dimensional dynamical systems 6971

37E05

Dynamical systems involving maps of the interval (piecewise continuous, continuous, smooth) 2417

37E10

Dynamical systems involving maps of the circle 839

37E15

Combinatorial dynamics (types of periodic orbits) 374

37E20

Universality and renormalization of dynamical systems [See also 37F25] 311

37E25

Dynamical systems involving maps of trees and graphs 400

37E30

Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 1161

37E35

Flows on surfaces 384

37E40

Dynamical aspects of twist maps 280

37E45

Rotation numbers and vectors 483

37E99

None of the above, but in this section 1347

37Fxx

Dynamical systems over complex numbers [See also 30D05, 32H50] 5056

37F05

Dynamical systems involving relations and correspondences in one complex variable 59

37F10

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets [See also 32A10, 32A20, 32H02, 32H04] 2297

37F12

Critical orbits for holomorphic dynamical systems 3

37F15

Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems 258

37F20

Combinatorics and topology in relation with holomorphic dynamical systems 311

37F25

Renormalization of holomorphic dynamical systems 187

37F31

Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics 3

37F32

Fuchsian and Kleinian groups as dynamical systems 4

37F34

Teichmüller theory; moduli spaces of holomorphic dynamical systems 5

37F35

Conformal densities and Hausdorff dimension for holomorphic dynamical systems 452

37F40

Geometric limits in holomorphic dynamics 42

37F44

Holomorphic families of dynamical systems; holomorphic motions; semigroups of holomorphic maps 6

37F46

Bifurcations; parameter spaces in holomorphic dynamics; the Mandelbrot and Multibrot sets 15

37F50

Small divisors, rotation domains and linearization in holomorphic dynamics 1194

37F75

Dynamical aspects of holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx] 575

37F80

Higher-dimensional holomorphic and meromorphic dynamics 5

37F99

None of the above, but in this section 522

37Gxx

Local and nonlocal bifurcation theory for dynamical systems [See also 34C23, 34K18] 8498

37G05

Normal forms for dynamical systems 819

37G10

Bifurcations of singular points in dynamical systems 939

37G15

Bifurcations of limit cycles and periodic orbits in dynamical systems 2222

37G20

Hyperbolic singular points with homoclinic trajectories in dynamical systems 301

37G25

Bifurcations connected with nontransversal intersection in dynamical systems 217

37G30

Infinite nonwandering sets arising in bifurcations of dynamical systems 35

37G35

Dynamical aspects of attractors and their bifurcations 495

37G40

Dynamical aspects of symmetries, equivariant bifurcation theory 553

37G99

None of the above, but in this section 3701

37Hxx

Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx] 2248

37H05

General theory of random and stochastic dynamical systems 176

37H10

Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15] 1154

37H12

Random iteration 6

37H15

Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx] 454

37H20

Bifurcation theory for random and stochastic dynamical systems [See also 37Gxx] 156

37H30

Stability theory for random and stochastic dynamical systems 11

37H99

None of the above, but in this section 408

37Jxx

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems [See also 53Dxx, 70Fxx, 70Hxx] 17879

37J06

General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants 33

37J11

Symplectic and canonical mappings 14

37J12

Fixed points and periodic points of finite-dimensional Hamiltonian and Lagrangian systems 3

37J20

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems 407

37J25

Stability problems for finite-dimensional Hamiltonian and Lagrangian systems 520

37J30

Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) 328

37J35

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 5276

37J37

Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures 12

37J38

Relations of finite-dimensional Hamiltonian and Lagrangian systems with algebraic geometry, complex analysis, special functions 9

37J39

Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) [See also 53D20] 30

37J40

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion 2254

37J46

Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems 40

37J51

Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods 22

37J55

Contact systems [See also 53D10] 108

37J60

Nonholonomic dynamical systems [See also 70F25] 446

37J65

Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) 3

37J70

Completely integrable discrete dynamical systems 5

37J99

None of the above, but in this section 5686

37Kxx

Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems [See also 35Axx, 35Qxx] 18113

37K06

General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws 30

37K10

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 10430

37K15

Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems 1157

37K20

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions [See also 14H70] 850

37K25

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry 675

37K30

Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures 990

37K35

Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 1953

37K40

Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 2798

37K45

Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems 484

37K50

Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 239

37K55

Perturbations, KAM for infinite-dimensional Hamiltonian and Lagrangian systems 464

37K58

Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems 6

37K60

Lattice dynamics; integrable lattice equations [See also 37L60] 1337

37K65

Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics 192

37K99

None of the above, but in this section 86

37Lxx

Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx] 4098

37L05

General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations 526

37L10

Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems 409

37L15

Stability problems for infinite-dimensional dissipative dynamical systems 347

37L20

Symmetries of infinite-dimensional dissipative dynamical systems 98

37L25

Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 264

37L30

Infinite-dimensional dissipative dynamical systems–attractors and their dimensions, Lyapunov exponents 1450

37L40

Invariant measures for infinite-dimensional dissipative dynamical systems 172

37L45

Hyperbolicity; Lyapunov functions for infinite-dimensional dissipative dynamical systems 79

37L50

Noncompact semigroups; dispersive equations; perturbations of infinite-dimensional dissipative dynamical systems 133

37L55

Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] 384

37L60

Lattice dynamics and infinite-dimensional dissipative dynamical systems [See also 37K60] 502

37L65

Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems 129

37L99

None of the above, but in this section 144

37Mxx

Approximation methods and numerical treatment of dynamical systems {For numerical analysis, see also 65Pxx; for software etc., see 37-04} 4956

37M05

Simulation of dynamical systems 1086

37M10

Time series analysis of dynamical systems 1264

37M15

Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems 1039

37M20

Computational methods for bifurcation problems in dynamical systems 575

37M21

Computational methods for invariant manifolds of dynamical systems 16

37M22

Computational methods for attractors of dynamical systems 12

37M25

Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) 625

37M99

None of the above, but in this section 467

37Nxx

Applications of dynamical systems 18197

37N05

Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx] 1604

37N10

Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10] 2045

37N15

Dynamical systems in solid mechanics [See mainly 74Hxx] 508

37N20

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 2645

37N25

Dynamical systems in biology [See also 92-XX] 6017

37N30

Dynamical systems in numerical analysis [See also 65-XX] 180

37N35

Dynamical systems in control [See also 93-XX] 2217

37N40

Dynamical systems in optimization and economics [See also 90-XX, 91-XX] 1343

37N99

None of the above, but in this section 1940

37Pxx

Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A44] 676

37P05

Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps 264

37P10

Arithmetic and non-Archimedean dynamical systems involving analytic and meromorphic maps 16

37P15

Dynamical systems over global ground fields 79

37P20

Dynamical systems over non-Archimedean local ground fields 136

37P25

Dynamical systems over finite ground fields 61

37P30

Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems [See also 11G50, 14G40] 123

37P35

Arithmetic properties of periodic points 86

37P40

Non-Archimedean Fatou and Julia sets 25

37P45

Families and moduli spaces in arithmetic and non-Archimedean dynamical systems 49

37P50

Dynamical systems on Berkovich spaces 43

37P55

Arithmetic dynamics on general algebraic varieties 99

37P99

None of the above, but in this section 19

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Mathematics Subject Classification – MSC2020

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