Abstract $\omega $-limit sets, chain recurrent sets, and basic sets for flows
نویسندگان
چکیده
منابع مشابه
Omega-limit Sets for Spiral Maps
We investigate a class of homeomorphisms of a cylinder, with all trajectories convergent to the cylinder base and one fixed point in the base. Let A be a nonempty finite or countable family of sets, each of which can be a priori an ω-limit set. Then there is a homeomorphism from our class, for which A is the family of all ω-limit sets.
متن کاملQuotient Sets and Density Recurrent Sets
Let S be a left amenable semigroup. Say that a subset A of S is large if there is some left invariant mean μ on S with μ(χA) > 0. A subset B of S is density recurrent if and only if, whenever A is a large subset of S, there is some x ∈ B such that x−1A ∩ A is large. We show that the set DR(S) of ultrafilters on S, every member of which is density recurrent, is a compact subsemigroup of the Ston...
متن کاملOmega-limit Sets for the Stein-ulam Spiral Map
In the late 1950’s, using computers in the Los Alamos National Laboratory, Stanis law Ulam and Paul Stein performed a comprehensive research on a class of quadratic maps of the 2-dimensional simplex ∆ to itself. Those maps arise in the theory of population genetics. One of them has the behavior much different than the 96 other ones. We call it the Stein-Ulam Spiral map. In 1972, S. Vallander as...
متن کاملRecurrent sets
A recurrent set of words is such that its minimal automaton is strongly connected. This class of sets does not seem to have been studied before. It contains the submonoids generated by prefix codes but also more general sets. We prove some properties of recurrent sets and investigate their relation with a natural generalization of prefix codes called weakly prefix codes, and also known as codes...
متن کاملOmega-limit Sets Close to Singular-hyperbolic Attractors
We study the omega-limit sets ωX(x) in an isolating block U of a singular-hyperbolic attractor for three-dimensional vector fields X. We prove that for every vector field Y close to X the set {x ∈ U : ωY (x) contains a singularity} is residual in U . This is used to prove the persistence of singular-hyperbolic attractors with only one singularity as chain-transitive Lyapunov stable sets. These ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0423423-x