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...f a [[topological dynamical system]] may be thought of heuristically as a “topological dynamical [[probability measure]]” of the subset. More precisely, its value ...em consists of a [[compact space|compact]] [[Hausdorff space|Hausdorff]] [[topological space]] ''X'' and a [[homeomorphism]] <math>T:X\rightarrow X</math>. Let <m ...

...em of [[Universal space#Universal spaces in topological dynamics|embedding topological  dynamical systems in shift spaces]] (over Euclidean cubes). A topological dynamical system consists of a compact Hausdorff topological space <math>\textstyle X</math> and a continuous self-map <math>\textstyle ...

...unded by some fixed constant. A similar definition exists in [[topological dynamics]]. Given a class <math>\textstyle \mathcal{C}</math> of topological spaces, <math>\textstyle \mathbb{U}\in\mathcal{C}</math> is '''universal''' ...

...small boundary property''' is a property of certain [[topological dynamics|topological dynamical systems]]. It is dynamical analog of the [[Inductive dimension|in Consider the category of '''topological dynamical system''' (''system'' in short) consisting of a compact metric sp ...

{{Short description|Totally disconnected topological space}} In [[mathematics]], '''Erdős space''' is a [[topological space]] named after [[Paul Erdős]], who described it in 1940.<ref name="erd ...

...t vector field]]. It has an enormous range of applications to the study of dynamics, including existence of [[periodic orbit]]s in [[Hamiltonian system]]s and ...omotopy type of the quotient space <math>(N_1/N_2,[N_2])</math>, seen as a topological pointed space. ...

...topology]], the '''mapping torus''' of a [[homeomorphism]] ''f'' of some [[topological space]] ''X'' to itself is a particular geometric construction with ''f''. ...do-Anosov homeomorphism]] of ''S''.<ref>W. Thurston, ''On the geometry and dynamics of diffeomorphisms of surfaces'', [[Bulletin of the American Mathematical S ...

...анализа в динамике твёрдого тела (Questions of qualitative analysis in the dynamics of a rigid body). At Moscow State University he became in 1983 a professor ...nsional manifolds <math>M</math> with genus greater than 1 (i.e. excluding topological spheres and tori) the geodetic flow (and general solutions of Hamilton's eq ...

...no |first4=Miguel |date=2021-10-12 |title=Integrable Systems and Spacetime Dynamics |url=https://link.aps.org/doi/10.1103/PhysRevLett.127.161601 |journal=Physi ...

...en-Av|first2=Radel|last3=Domany|first3=Eytan|date=1990-08-20|title=Cluster dynamics for fully frustrated systems|url=https://link.aps.org/doi/10.1103/PhysRevLe ....|last2=Wang|first2=Jian-Sheng|date=1987-01-12|title=Nonuniversal critical dynamics in Monte Carlo simulations|url=https://link.aps.org/doi/10.1103/PhysRevLett ...

...k | title=Recent Advances in Topological Dynamics (Proc. Conf. Topological Dynamics, Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund) | p ...

...irst2=Masahito|title=Spinor Bose gases: Symmetries, magnetism, and quantum dynamics|journal=Reviews of Modern Physics|volume=85|issue=3|year=2013|pages=1191–12 [[ground state]]s, non-equilibrium dynamics, and ...

...iting a certain type of bifurcation are locally (around the equilibrium) [[topological conjugacy|topologically equivalent]] to the normal form of the bifurcation. ...-1, \mu = r + 1 </math>.<ref name="strogatz">Strogatz, Steven. "Nonlinear Dynamics and Chaos". Westview Press, 2001. p. 52.</ref> ...

...nu–White–Fuller formula]] <math>Lk = Wr + Tw</math> in [[topological fluid dynamics]] (for its close relation to [[Hydrodynamical helicity|kinetic]] and [[magn ..., R.L.]] (2005) Inflexional disequilibrium of magnetic flux tubes. ''Fluid Dynamics Research'' '''36''', 319-332. ...

...ally injective on ''e''. Train-track maps are a key tool in analyzing the dynamics of [[automorphism]]s of [[finitely generated group|finitely generated]] [[f ...Martin Lustig, ''Automorphisms of free groups have asymptotically periodic dynamics.'' [[Crelle's Journal]], vol. 619 (2008), pp. 1&ndash;36, {{doi|10.1515/CR ...

...al and biological properties, such as those arising in [[topological fluid dynamics]], [[DNA]] modeling and in [[material science]]. ...

...c moments]] of atomic cores. A '''magnetic skyrmionium''' is a ring-shaped topological spin texture and is closely related to the [[magnetic skyrmion]].<ref>{{Cit == Topological charge == ...

...t2=Wei|last3=Chitra|first3=R.|title=Generating quantum multicriticality in topological insulators by periodic driving|journal=Physical Review B|year=2020|volume=1 ...l). The vertical red lines depict topological phase boundaries. Across the topological phase transitions, the Berry connection diverges and flips sign around the ...

...local. However, networks differ not only in their range but also in their topological structure. It is possible to distinguish: ...Strogatz (WS) model]].<ref>Watts, J.D. and H.S.Strogatz (1998). Collective dynamics of 'small-world' networks, Nature, Vol.393, p.440-442</ref> All aforementio ...

...rrespondence''', which connected structural Ramsey theory to [[topological dynamics]]. ...tween structural Ramsey theory, Fraïssé theory, and ideas from topological dynamics. ...