37-XX Dynamical systems and ergodic theory [See also 26A18, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
37-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
37-01 Instructional exposition (textbooks, tutorial papers, etc.)
37-02 Research exposition (monographs, survey articles)
37-03 Historical {!must also be assigned at least one classification number from section 01}
37-04 Explicit machine computation and programs (not the theory of computation or programming)
37-06 Proceedings, conferences, collections, etc.
37Axx Ergodic theory
37A05 Measure-preserving transformations
37A10 One-parameter continuous families of measure-preserving transformations
37A15 General groups of measure-preserving transformation [See mainly 22Fxx]
37A17 Homogeneous flows [See also 22Fxx]
37A20 Orbit equivalence, cocycles, ergodic equivalence relations
37A25 Ergodicity, mixing, rates of mixing
37A30 Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35}
37A35 Entropy and other invariants, isomorphism, classification
37A40 Nonsingular (and infinite-measure preserving) transformations
37A45 Relations with number theory and harmonic analysis [See also 11Kxx]
37A50 Relations with probability theory and stochastic processes
37A55 Relations with the theory of C*-algebras [See mainly 46L55]
37A60 Dynamical systems in statistical mechanics [See also 82Cxx]
37A99 None of the above, but in this section
37Bxx Topological dynamics [See also 54H20]
37B05 Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37B10 Symbolic dynamics [See also 37Cxx, 37Dxx]
37B15 Cellular automata
37B20 Notions of recurrence
37B25 Lyapunov functions and stability; attractors, repellers
37B30 Index theory, Morse - Conley indices
37B35 Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
37B40 Topological entropy
37B45 Continua theory in dynamics
37B50 Multi-dimensional shifts of finite type, tiling dynamics
37B55 Nonautonomous dynamical systems
37B99 None of the above, but in this section
37Cxx Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
37C05 Smooth mappings and diffeomorphisms
37C10 Vector fields, flows, ordinary differential equations
37C15 Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37C20 Generic properties, structural stability
37C25 Fixed points, periodic points, fixed-point index theory
37C30 Zeta functions, (Ruelle - Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
37C35 Orbit growth
37C40 Smooth ergodic theory, invariant measures [See also 37Dxx]
37C45 Dimension theory of dynamical systems
37C50 Approximate trajectories (pseudotrajectories, shadowing, etc.)
37C55 Periodic and quasiperiodic flows and diffeomorphisms
37C60 Nonautonomous smooth dynamical systems [See also 37B50]
37C65 Monotone flows
37C70 Attractors and repellers, topological structure
37C75 Stability theory
37C80 Symmetries, equivariant dynamical systems
37C85 Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx]
37C99 None of the above, but in this section
37Dxx Dynamical systems with hyperbolic behavior
37D05 Hyperbolic orbits and sets
37D10 Invariant manifold theory
37D15 Morse - Smale systems
37D20 Uniformly hyperbolic systems (expanding, Anosov, axiom A, etc.)
37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D30 Partially hyperbolic systems and dominated splittings
37D35 Thermodynamic formalism, variational principles, equilibrium states
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37D45 Strange attractors, chaotic dynamics
37D50 Hyperbolic systems with singularities (billiards, etc.)
37D99 None of the above, but in this section
37Exx Low-dimensional dynamical systems
37E05 Maps of the interval (piecewise continuous, continuous, smooth)
37E10 Maps of the circle
37E15 Combinatorial dynamics (types of periodic orbits)
37E20 Universality, renormalization [See also 37F25]
37E25 Maps of trees and graphs
37E30 Homeomorphism and diffeomorphisms of plane and surfaces
37E35 Flows on surfaces
37E40 Twist maps
37E45 Rotation numbers and vectors
37E99 None of the above, but in this section
37Fxx Complex dynamical systems [See also 30D05, 32Hxx]
37F05 Relations and correspondences
37F10 Polynomials; rational maps; entire and meromorphic functions
37F15 Expanding maps; hyperbolicity; structural stability
37F20 Combinatorics and topology
37F25 Renormalization
37F30 Quasiconformal methods and Teichm\"uller theory; Fuchsian and Kleinian groups as dynamical systems
37F35 Conformal densities and Hausdorff dimension
37F40 Geometric limits
37F45 Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
37F50 Small divisors, rotation domains and linearization; Fatou and Julia sets
37F75 Holomorphic foliations and vector fields
37F99 None of the above, but in this section
37Gxx Local and global bifurcation theory
37G05 Normal forms
37G10 Bifurcations of singular points
37G15 Bifurcations of limit cycles and periodic orbits
37G20 Hyperbolic singular points with homoclinic trajectories
37G25 Bifurcations connected with nontransversal intersection
37G30 Infinite nonwandering sets
37G35 Attractors and their bifurcations arising in bifurcations
37G40 Symmetries, equivariant bifurcation theory
37G99 None of the above, but in this section
37Hxx Random dynamical systems
37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]
37H10 Generation, random and stochastic difference and differential equations [See also 34K50, 37F05, 60Hxx]
37H15 Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]
37H20 Bifurcation theory [See also 37Gxx]
37H99 None of the above, but in this section
37Jxx Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Hxx]
37J05 General theory, relations with symplectic geometry and topology
37J10 Symplectic mappings, fixed points
37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]
37J20 Bifurcation problems
37J25 Stability problems
37J30 Obstructions to integrability (nonintegrability criteria)
37J35 Completely integrable systems, topological structure of phase space, integration methods
37J40 Perturbations, normal forms, small divisors, KAM theory, Arnold diffusion
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
37J50 Action-minimizing orbits and measures for Lagrangian systems
37J55 Contact systems [See also 53D10]
37J60 Nonholonomic dynamical systems [See also 70F25]
37J99 None of the above, but in this section
37Kxx Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
37K15 Integration of completely integrable systems by inverse spectral and scattering methods
37K20 Relations with algebraic geometry, complex analysis, special functions [See also 14H70]
37K25 Relations with differential geometry
37K30 Relations with infinite-dimensional Lie algebras and other algebraic structures
37K35 Lie - B\"acklund and other transformations
37K40 Soliton theory, asymptotic behavior of solutions
37K45 Stability problems
37K50 Bifurcation problems
37K55 Perturbations, KAM for infinite-dimensional systems
37K60 Lattice dynamics [See also 37L60]
37K65 Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
37K99 None of the above, but in this section
37Lxx Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]
37L05 General theory, nonlinear semigroups, evolution equations
37L10 Normal forms, center manifold theory, bifurcation theory
37L15 Stability problems
37L20 Symmetries
37L25 Inertial manifolds and other invariant attracting sets
37L30 Attractors and their dimensions, Lyapunov exponents
37L40 Invariant measures
37L45 Hyperbolicity; Lyapunov functions
37L50 Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
37L55 Infinite-dimensional random dynamical systems; stochastic equations
37L60 Lattice dynamics [See also 37K60]
37L65 Approximation methods (nonlinear Galerkin, etc.)
37L99 None of the above, but in this section
37Mxx Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]
37M05 Simulation
37M10 Time series analysis
37M15 Symplectic integrators
37M20 Computation of homoclinic cycles
37M25 Computational methods for bifurcation problems
37M30 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)
37M99 None of the above, but in this section
37Nxx Applications
37N05 Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]
37N10 Dynamical systems in fluid mechanics and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]
37N15 Dynamical systems in solid mechanics [See mainly 74Hxx]
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
37N25 Dynamical systems in biology [See mainly 92-XX, but also 91-XX]
37N30 Dynamical systems in numerical analysis
37N35 Dynamical systems in control
37N40 Dynamical systems in optimization and economics
37N99 None of the above, but in this section