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Navegando por la clasificación temática MSC 2000: 37 · Dynamical systems and ergodic theory
 
37 Dynamical systems and ergodic theory
  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
  37-04 Explicit machine computation and programs (not the theory of computation or programming)
  37-06 Proceedings, conferences, collections, etc.
  37-99 Dynamical systems and ergodic theory (not classified at a more specific level)
 
  37A Ergodic theory [See also 28Dxx]
    37A05 Measure-preserving transformations
    37A10 One-parameter continuous families of measure-preserving transformations
    37A15 General groups of measure-preserving transformations [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 [See also 60Fxx and 60G10]
    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
 
  37B 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
 
  37C 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
    37C27 Periodic orbits of vector fields and flows
    37C29 Homoclinic and heteroclinic orbits
    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 37B55]
    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, and also 57R30, 57Sxx]
    37C99 None of the above, but in this section
 
  37D 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
 
  37E 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 Homeomorphisms and diffeomorphisms of planes and surfaces
    37E35 Flows on surfaces
    37E40 Twist maps
    37E45 Rotation numbers and vectors
    37E99 None of the above, but in this section
 
  37F Complex dynamical systems [See also 30D05, 32H50]
    37F05 Relations and correspondences
    37F10 Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
    37F15 Expanding maps; hyperbolicity; structural stability
    37F20 Combinatorics and topology
    37F25 Renormalization
    37F30 Quasiconformal methods and Teichmüller 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 [See also 32M25, 32S65, 34Mxx]
    37F99 None of the above, but in this section
 
  37G Local and nonlocal bifurcation theory [See also 34C23, 34K18]
    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 arising in bifurcations
    37G35 Attractors and their bifurcations
    37G40 Symmetries, equivariant bifurcation theory
    37G99 None of the above, but in this section
 
  37H Random dynamical systems [See also 15A52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]
    37H05 Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]
    37H10 Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]
    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
 
  37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 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
    37J55 Contact systems [See also 53D10]
    37J60 Nonholonomic dynamical systems [See also 70F25]
    37J99 None of the above, but in this section
 
  37K 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-Bäcklund 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
 
  37L 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 [See also 35R60, 60H10, 60H15]
    37L60 Lattice dynamics [See also 37K60]
    37L65 Special approximation methods (nonlinear Galerkin, etc.)
    37L99 None of the above, but in this section
 
  37M Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]
    37M05 Simulation
    37M10 Time series analysis
    37M15 Symplectic integrators
    37M20 Computational methods for bifurcation problems
    37M25 Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)
    37M99 None of the above, but in this section
 
  37N Applications
    37N05 Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]
    37N10 Dynamical systems in fluid mechanics, oceanography 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
 

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