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[[Category:Theorems in mathematical physics]] [[Category:Theorems in dynamical systems]] ...

{{Short description|Theorem in dynamical systems theory}} ...act space|compact]] two-dimensional [[manifold]]s, [[structurally stable]] systems may be characterized by the following properties: ...

The '''Chetaev instability theorem''' for [[dynamical system]]s states that if there exists, for the system <math>\dot{\textbf{x} ...gin such that <math>\dot{V}(\textbf{x})>0</math> for all <math>\mathbf{x} \in G \cap U</math> ...

[[:Category:Dynamical systems|Dynamical&nbsp;systems]] | ...| [[:Category:Mathematical proofs|Proofs]] | [[:Category:Unsolved problems in mathematics|Unsolved problems ]] ...

...m of curves]] describes classification of [[Regular curve|regular curves]] in space up to [[Translation (geometry)|translation]] and [[rotation]]. ...as a stepping stone to a larger result, rather than as a useful statement in-and-of itself. ...

{{short description|Stability criterion for a dynamical system with a partially known characteristic polynomial}} ...all [[root]]s have negative real parts). Kharitonov's theorem can be used in the case where the coefficients are only known to be within specified range ...

...{{cite book |first=Michael |last=Shub |title=Global Stability of Dynamical Systems |publisher=Springer |year=1987 |pages=65–66 |url=https://books.google.com/b ...-link=Gerald Teschl| title = Ordinary Differential Equations and Dynamical Systems| publisher=[[American Mathematical Society]]| place = [[Providence, Rhode I ...

In [[mathematics]], a '''classification theorem''' answers the [[classificatio ...p in solving it. (A combination of invariant values is realizable if there in fact exists an object whose invariants take on the specified set of values) ...

{{Short description|Theorem on the behavior of dynamical systems}} ...inson |chapter=The Poincaré–Bendixson Theory of Two-Dimensional Autonomous Systems |title=Theory of Ordinary Differential Equations |url=https://archive.org/d ...

...to [[semisimple Lie group]]s by V. A. Kaimanovich and further generalized in the works of [[David Ruelle]], [[Grigory Margulis]], [[Anders Karlsson (mat ...multiplicative ergodic theorem is stated in terms of matrix cocycles of a dynamical system. The theorem states conditions for the existence of the defining lim ...

{{Short description|Concept in the analysis of dynamical systems}}{{No footnotes|date=October 2023}} ...of [[dynamical system]]s and [[control theory]]. A similar concept appears in the theory of general state-space [[Markov chain]]s usually under the name ...

{{Short description|Set of points linked through the evolution function of a dynamical system}} {{About|orbits in dynamical systems theory||Orbit (disambiguation)}} ...

In [[mathematics]], '''topology''' (from the [[Greek language|Greek]] words {{ ...istance or metric defines a topology. The deformations that are considered in topology are [[homeomorphism]]s and [[homotopy|homotopies]]. A property tha ...

In [[mathematics]], the '''Ornstein isomorphism theorem''' is a deep result in [[ergodic theory]]. It states that if two [[Bernoulli scheme]]s have the s | journal=[[Advances in Mathematics]] ...

In [[mathematics]], more specifically in the study of [[dynamical system]]s and [[differential equation]]s, a '''Liénard equation'''<ref>Lién ...arLienardSystems/ Phase Curve And VectorField For Piecewise Linear Lienard Systems]</ref> ...

...vs|txt|authorlink=Arnaud Denjoy|last=Denjoy|year=1932}} proved the theorem in the course of his topological classification of [[homeomorphism]]s of the c [[Category:Dynamical systems]] ...

In [[mathematics]], a '''prime geodesic''' on a [[hyperbolic geometry|hyperbol ...section presents some facts from [[hyperbolic geometry]] that are helpful in understanding prime geodesics. ...

{{Short description|In mathematics, a concept that formalizes a certain idea of movement and mixin ...g sets in phase space was introduced by [[George David Birkhoff|Birkhoff]] in 1927.{{citation needed|date=November 2010}} ...

In [[mathematics]], the '''Bendixson–Dulac theorem''' on [[dynamical system]]s states that if there exists a <math>C^1</math> [[function (mathem has the same sign (<math>\neq 0</math>) [[almost everywhere]] in a [[simply connected]] region of the plane, then the [[plane autonomous sys ...

{{Short description|Test for whether a polynomial's roots lie in the left-half complex plane}} .... [[Derivation of the Routh array|The Routh–Hurwitz theorem was proved]] in 1895, and it was named after [[Edward John Routh]] and [[Adolf Hurwitz]]. ...