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...s theorem on dynamical systems''' is a result on stability of solutions of systems of [[differential equation]]s. It has applications to [[chemical kinetics] [[Category:Theorems in dynamical systems]] ...

In mathematics, particularly in the study of functions of [[several complex variable]]s, '''Ushiki's theore ...ompact space|compact]] [[smooth function|smooth]] [[invariant manifold]]. In particular, such a map cannot have a [[homoclinic connection]] or [[heteroc ...

...[differential equation]]s. The result was established by [[Czesław Olech]] in 1963,<ref>{{cite journal |first=Czesław |last=Olech |title=On the Global St ...= f ( \mathbf{x} )</math>, <math>\mathbf{x} = [ x_1 \, x_2]^{\mathsf{T}} \in \mathbb{R}^2</math>, where <math>f(\mathbf{x}) = \begin{bmatrix} f^1 (\math ...

...dimension]] is bounded by some fixed constant. A similar definition exists in [[topological dynamics]]. ...the case <math>\textstyle d=1</math> of the following theorem. The theorem in full generality was proven by Nöbeling. ...

{{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. ...

...4 November 1943, [[Moscow]]) is a Russian mathematician, specializing in [[dynamical system]]s, [[differential equation]]s, and complex [[foliation]]s. Ilyashenko received in 1969 from [[Moscow State University]] his Russian candidate degree (Ph.D.) ...

In mathematics, a '''Lagrangian system''' is a pair {{math|(''Y'', ''L'')}}, c ...h> if a reference frame is fixed. In [[classical field theory]], all field systems are the Lagrangian ones. ...

...e=Lyapunov–Malkin Theorem and Stabilization of the Unicycle Rider |journal=Systems and Control Letters |volume=45 |issue=4 |pages=293–302 |doi=10.1016/S0167-6 In the system of [[differential equation]]s, ...

...le–Arnold theorem''' states that if, in a [[Hamiltonian system|Hamiltonian dynamical system]] with ''n'' [[Degrees of freedom (mechanics)|degrees of freedom]], ...T. Jones|editor2=Alexander I. Khibnik|title=Multiple-Time-Scale Dynamical Systems|url=https://books.google.com/books?id=LYLkBwAAQBAJ&pg=PA1|year=2012|publish ...

In [[mathematics]], '''Gauss congruence''' is a property held by certain [[seq Sequences satisfying Gauss congruence naturally occur in the study of [[topological dynamics]], [[algebraic number theory]] and [[co ...

...th>, it suffices that the ergodicity condition be valid for initial states in a set <math>B(\mu)</math> of positive [[Lebesgue measure]].<ref name='bonat ...>{{cite journal|last1=Sinai|first1=Yakov G.|year=1972|title=Gibbs measures in ergodic theory|journal=Russian Mathematical Surveys|volume=27|issue=4|pages ...

...n the [[complex numbers]] into itself. The result was proved independently in 1926 by the French mathematician [[Arnaud Denjoy]] and the Dutch mathematic ...t on the Poincaré disk|hyperbolic disks]] centered on ''z'', if ''z'' lies in ''D'', and disks tangent to the unit circle at ''z'', if ''z'' lies on the ...

...chnical tool for studying stable maps. Since then it has proved important in its own right. Roughly speaking, two map germs ''&fnof;'',&nbsp;''g'' are ...'' to the graph of ''g'', as well as the graph of the zero map to itself. In particular, the diffeomorphism &phi; maps ''f''^&minus;1(0) to '' ...

...CCM is based on the theory of [[dynamical system]]s and can be applied to systems where causal variables have synergistic effects. As such, CCM is specifical ...h>M</math>, preserving instrinsic state space properties of <math>M</math> in <math>M_X</math>. ...

| caption = Yael Dowker in New Orleans, 1961. | thesis_title = The Ergodic Theorems and Invariant Measure ...

...ure whose intersection with each fiber is singular (at most a single point in [[Anatole Katok|Katok's]] example). There is no real contradiction to Fubin ...fiber-wise proofs for center foliations of partially hyperbolic dynamical systems: these foliations are typically Hölder but not absolutely continuous. ...

...nineteenth century, [[Sophus Lie]] introduced the notion of [[Lie group]] in order to study the solutions of [[ordinary differential equations]]<ref nam ...maps every solution of the system to another solution of the same system. In other words, it maps the solution set of the system to itself. Elementary e ...

...o Kakutani]]. The lemma is used extensively in ergodic theory, for example in [[Ornstein isomorphism theorem|Ornstein theory]] and has many generalizatio ...is which are traditionally called lemmas despite the fact that their roles in their respective fields are fundamental. ...

...group]] and <math>\Gamma</math> a [[lattice (discrete subgroup)|lattice]] in it. ...=Host |first1=Bernard |last2=Kra |first2=Bryna |title=Nilpotent Structures in Ergodic Theory |date=12 December 2018 |publisher=American Mathematical Soc. ...

...considered a methodology for [[data modeling]], [[predictive analytics]], dynamical system analysis, [[machine learning]] and [[Time series|time series analysi ...mes. However, real-world systems are often nonlinear and multidimensional, in some instances rendering explicit equation-based modeling problematic. Empi ...