Search results

{{wiktionary|dynamics|dynamic}} '''Dynamics''' (from [[Greek language|Greek]] δυναμικός ''dynamikos'' "powerful", from ...

...opological property]]. Basic examples of topological properties are: the [[topological dimension|dimension]], which allows distinguishing between a [[line (geomet ...it was not until the first decades of the 20th century that the idea of a topological space was developed. ...

* a property in thermodynamics and fluid dynamics, see [[Compressibility]] or [[Incompressible flow]] * a topological property, see [[Incompressible surface]] ...

...erated function]]s and more generally [[dynamical systems]], since, if the dynamics of one iterative function can be determined, then that for a topologically ...math>, and <math> h\colon Y \to X</math> are [[continuous function]]s on [[topological space]]s, <math> X </math> and <math> Y</math>. ...

...iterates. An important '''variational principle''' relates the notions of topological and measure-theoretic entropy. ...y)|continuous]] self-map ''f''&nbsp;:&nbsp;''X''&nbsp;→&nbsp;''X''. Its '''topological entropy''' is a nonnegative [[extended real number]] that can be defined in ...

==Dynamics== ...ehavior followed by stress relaxations due to particle rearrangements. The dynamics of these systems are highly nonlinear in nature. The increase in stress by ...

*[[System dynamics]], [[system analysis]] *[[Symbolic dynamics]] ...

...Durham, retrieved 28 February 2016.</ref> He specialises in the study of [[topological soliton]]s. ...2006 for contributions to the study of [[topological soliton]]s and their dynamics.<ref>[https://www.ams.org/notices/200609/people.pdf Mathematics People, AMS ...

{{Short description|Class of compact connected topological spaces}} :''This page discusses a class of topological groups. For the wrapped loop of wire, see [[Solenoid]].'' ...

...construction, and it is applied to encode the combinatorics and [[symbolic dynamics]] of the covering, and provide examples of [[self-similar group]]s. ...ected]] and [[Connected space#Local connectedness|locally path-connected]] topological space ''X'' by its subset <math>X_1</math>, ...

...functions in topology|Spread (topology)]], a cardinal function defined on topological spaces, also known as the hereditary cellularity * Spreading dynamics, the wetting of a surface, see [[Wetting#Spreading dynamics]] ...

In [[mathematics]], the '''rotation number''' is an [[Topological property|invariant]] of [[homeomorphism]]s of the [[circle]]. ....}} Intuitively, it measures the average rotation angle along the [[orbit (dynamics)|orbits]] of {{mvar|f}}. ...

..., a '''phase portrait''' is a [[geometric]] representation of the [[orbit (dynamics)|orbit]]s of a [[dynamical system]] in the [[phase plane]]. Each set of ini ...ent for the chosen parameter value. The concept of [[topological conjugacy|topological equivalence]] is important in classifying the behaviour of systems by speci ...

...] Lecturer (''New Connections Between Logic, Ramsey Theory and Topological Dynamics'') <ref>[https://math.berkeley.edu/2004-tarski-lectures 2004 Tarski Lecture .... Pestov and S. Todorcevic, "Fraïssé limits, Ramsey theory and topological dynamics of automorphism groups", Geometric and Functional Analysis 15 (1) (2005), 1 ...

...ass of [[dynamical system]]s which have been extensively studied and whose dynamics is relatively well understood. A prominent example is the [[Smale horseshoe ...lic diffeomorphisms''', because the portion of ''M'' where the interesting dynamics occurs, namely, ''&Omega;''(''f''), exhibits hyperbolic behavior. ...

...d Witten]] and [[Cumrun Vafa]], by analogy with Witten's earlier idea of [[topological quantum field theory]]. ...lues are protected by [[spacetime]] supersymmetry. Various calculations in topological string theory are closely related to [[Chern–Simons theory]], [[Gromov–Witt ...

...an invariant set in the [[phase space]] of a [[dynamical system]]. It is a topological circle of [[equilibrium point|equilibrium points]] and connecting [[heteroc ...ext of rotating convection, and as three competing species in [[population dynamics]]. ...

...ogy. In higher dimensions, this is no longer true, indicating that typical dynamics can be very complex (cf. [[strange attractor]]). An important class of stru ...tor fields and flows: in this setting, the homeomorphism ''h'' must be a [[topological conjugacy]]. ...

{{short description|Aspect of Eulerian fluid dynamics}} {{about|fluid dynamics|magnetic fields|magnetic helicity|particle physics|helicity (particle physi ...

...e standard."<ref>{{cite book |last=Strogatz |first=Steven |title=Nonlinear Dynamics and Chaos |year=2001 |publisher=Westview Press |isbn=0-7382-0453-6 |url-acc * The dynamics on the invariant set can be represented via [[symbolic dynamics]], ...