One of the invariants in [[Ergodic theory|ergodic theory]], the construction of which recalls the construction of the cohomology of
...single non-trivial example. The use of "homological" concepts in ergodic theory stems from the fact that in many real cases it may be important to know (an
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$#C+1 = 63 : ~/encyclopedia/old_files/data/A011/A.0101680 Algebraic systems, quasi\AAhvariety of
A class of algebraic systems ( $ \Omega $-
6 KB (881 words) - 16:10, 1 April 2020
...an 4 cannot, in general, be solved by radicals (see [[Galois theory|Galois theory]]).
...Many questions of the theory of radicals have been studied within category theory. See also [[Radical of a group|Radical of a group]]; [[Radical in a class o
2 KB (254 words) - 16:33, 19 April 2014
Many dynamical systems (cf. [[Dynamical system|Dynamical system]]) are described by difference equ
or by autonomous systems of differential equations (cf. [[Autonomous system|Autonomous system]]) $
6 KB (764 words) - 08:03, 6 June 2020
A shift operator is used, in particular, in the theory of dynamical systems (see [[Shift dynamical system|Shift dynamical system]]; [[Bernoulli automor
...e often easy to analyze. They are of great importance in dynamical systems theory, owing to the Smale–Birkhoff theorem: A discrete-time [[Dynamical system|
3 KB (392 words) - 08:13, 6 June 2020
...s is given in [[#References|[a1]]]. A general consideration of supertriple systems is given in [[#References|[a2]]] and [[#References|[a5]]].
...]</td> <td valign="top"> W.G. Lister, "A structure theory of Lie triple systems" ''Trans. Amer. Math. Soc.'' , '''72''' (1952) pp. 217–242</td></tr><t
3 KB (559 words) - 16:43, 15 March 2023
$#C+1 = 91 : ~/encyclopedia/old_files/data/A011/A.0101670 Algebraic systems, class of
A class of algebraic systems of the same type. All systems of a given type are assumed to be written in a given signature $ \Omega $
8 KB (1,165 words) - 16:10, 1 April 2020
is described by several systems of differential equations
...etails see [[#References|[3]]]). The participation of several differential systems $ ( S _ {i} ) $
4 KB (557 words) - 08:26, 6 June 2020
''in control theory''
...ates have this property. The accessibility property is typical for control systems. Namely, every control system defined on a smooth manifold by a pair of smo
2 KB (329 words) - 15:33, 20 November 2014
...ems theory. For systems in the sense of logics, see [[Formal_system|formal systems]].
...cussed at the interplay between them (e.g. cybernetic models of biological systems). A more fundamental definition of a system was required encompassing the
8 KB (1,362 words) - 17:44, 25 September 2012
...6]]]. L. Neustadt has shown the significance of these operators in control theory [[#References|[a6]]].
...on abstract Volterra operators and associated equations. However, a solid theory of this kind of operator does not yet exist.
6 KB (863 words) - 15:34, 13 July 2014
...TD> <TD valign="top"> A.N. Sharkovskii, V.A. Dobrynskii, , ''Dynamical systems and problems of stability of solutions of differential equations'' , Kiev
...dy of hyperbolic sets (cf. [[Hyperbolic set|Hyperbolic set]]) in dynamical systems; see Chapt. 2 in [[#References|[a2]]].
3 KB (395 words) - 10:06, 24 August 2014
$#C+1 = 1 : ~/encyclopedia/old_files/data/A014/A.0104080 Automata, theory of
...[[Algorithms, theory of|Algorithms, theory of]]), particularly so with the theory of abstract machines, since automata can be regarded as a special case of s
7 KB (975 words) - 18:49, 5 April 2020
== In dynamical systems ==
4 KB (608 words) - 11:50, 1 May 2023
A property of an axiom system for a given axiomatic theory, defined as follows: Every axiom in the system is independent, i.e. it is n
...endent if and only if there is an [[Interpretation|interpretation]] of the theory in which the axiom is false, while all the other axioms are true. The const
3 KB (478 words) - 17:19, 7 February 2011
...is important to note that if the equations of some of the elements of the systems are unknown, the Nyquist diagram can be constructed experimentally, by feed
...ce been developed for multivariable, infinite-dimensional and sampled-data systems, e.g. [[#References|[5]]], , , .
4 KB (619 words) - 13:06, 10 August 2014
...ase the theory of representations of infinite groups is connected with the theory of representations of the group algebras of these groups.
...> <TD valign="top"> B.I. Plotkin, "Groups of automorphisms of algebraic systems" , Wolters-Noordhoff (1972)</TD></TR></table>
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...c); [[Qualitative theory of differential equations]]; [[Poincaré–Bendixson theory]].
* {{Ref|a1}} O. Hajek, "Dynamical systems in the plane", Acad. Press (1968)
535 bytes (71 words) - 14:12, 8 April 2023
...erent Perron transformations [[#References|[1]]], [[#References|[2]]]. For systems (2) with bounded continuous coefficients, all the Perron transformations ar
...TR><TR><TD valign="top">[4]</TD> <TD valign="top"> N.A. Izobov, "Linear systems of ordinary differential equations" ''J. Soviet Math.'' , '''5''' : 1 (1
3 KB (408 words) - 19:31, 11 January 2024
''in the theory of dynamical systems, discrete-time dynamical system''
...y investigated, although in applications, mostly continuous-time dynamical systems (cf. [[Flow (continuous-time dynamical system)|Flow (continuous-time dynami
3 KB (418 words) - 05:47, 18 May 2022