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...range stability''' is a concept in the [[stability theory]] of [[dynamical systems]], named after [[Joseph-Louis Lagrange]]. ...th>\gamma_x^+, \gamma_x^-</math> and <math>\gamma_x</math> being [[bounded set|bounded]], respectively. ...

...nvertible systems is used in formulating a precise mathematical definition of an [[attractor]]. === Conley index theory === ...

...between the states of the system which is compatible with the transitions of the system. ...lization of the Procedure of Karp and Miller to Well Structured Transition Systems". ...

{{Short description|Class of graph dynamical systems}} [[File:SDSphase1.png|thumbnail|right|Phase space of the sequential dynamical system]] ...

...ystems. They are named after [[Marston Morse]], the creator of the [[Morse theory]], and [[Stephen Smale]], who emphasized their importance for smooth dynami ...e number of singular points (i.e. equilibrium points of the flow), and all of them are [[Hyperbolic equilibrium point|hyperbolic equilibrium points]]. ...

...have the ''K''-property, although more recent research has shown that many of these are in fact Bernoulli automorphisms. ...; whereas the ''B''-automorphisms are 'completely' described by [[Ornstein theory]]. ...

...emma describing the behaviour of pseudo-orbits near a hyperbolic invariant set}} ...://linkinghub.elsevier.com/retrieve/pii/S0021999121002849 |journal=Journal of Computational Physics |language=en |volume=440 |pages=110389 |arxiv=2010.13 ...

{{About|the topic in dynamical systems|the topic in constrained optimization|barrier function}} ...brid systems using barrier certificates." International Workshop on Hybrid Systems: Computation and Control. Springer, Berlin, Heidelberg, 2004. ...

{{Short description|Theorem in dynamical systems theory}} ...bifurcation theory]]. Conley index theory formed the basis for development of [[Floer homology]]. ...

{{Short description|Type of dynamical system}} ...g | last2=Shi-Ping | first2=Yang | last3=Hu | first3=Liu | title=Targeting of Kolmogorov–Arnold–Moser Orbits by the Bailout Embedding Method in Two Coupl ...

{{Short description|Axiomatic set theory}} ...eory]], without substantially weakening the [[axiom of comprehension|axiom of unrestricted comprehension]]. ...

...ble inputs.<ref name=ANDERSON>Brian D. O Anderson, "A Simplified Viewpoint of Hyperstability", ''IEEE Transactions on Automatic Control, June 1968''<!-- ...constants <math>k_1 \ge 0, k_2 \ge 0</math> such that any state trajectory of the system satisfies the inequality: ...

...losure''' of a [[binary relation]] <math>R</math> on a [[Set (mathematics)|set]] <math>X</math> is the smallest [[symmetric relation]] on <math>X</math> t ...e of <math>R</math> is the relation "<math>x</math> is a parent or a child of <math>y</math>". ...

{{Short description|System in mathematical set theory}} In [[mathematics]], '''vague sets''' are an extension of [[fuzzy set]]s. ...

...nate]]. An example is the [[number line]], each [[point (geometry)|point]] of which is described by a single [[real number]].<ref>{{cite web|url=http://f ...r smooth [[curve]] is a one-dimensional space, regardless of the dimension of the [[ambient space]] in which the line or curve is embedded. Examples incl ...

...phenomena, and has close ties to the theories of [[optimal control]] and [[set-valued analysis]]. .... Viability theory started in 1976 by translating mathematically the title of the book [[Chance and Necessity]]<ref>{{cite book |author=Jacques Monod |ye ...

...ibrium]], and in which state variables called [[Extent of reaction|extents of reaction]] are allowed, but [[thermodynamic equilibrium|thermodynamic equil ...ements of the [[Le Chatelier principle]] can be interpreted. With the help of RERs the equilibrium coupling was defined.<ref>[http://pubs.acs.org/doi/abs ...

...Frege systems (more often known as [[Hilbert system]]s in general [[proof theory]]) are named after [[Gottlob Frege]]. ...intended to capture the properties of the most common propositional proof systems.<ref name=":0" /> ...

...It is dynamical analog of the [[Inductive dimension|inductive definition]] of [[Lebesgue covering dimension]] zero. ..._{T}(X),\ \mu(E)=0</math> where <math>M_T(X)</math> denotes the collection of <math>T</math>-[[invariant measure]]s on <math>X</math>. ...

....</math> A relation is called {{em|reflexive}} if it relates every element of <math>X</math> to itself. ...s "<math>x</math> is less than <math>y</math>", then the reflexive closure of <math>R</math> is the relation "<math>x</math> is less than or equal {{nowr ...