14,784 research outputs found
Genericity in Topological Dynamics
We study genericity of dynamical properties in the space of homeomorphisms of
the Cantor set and in the space of subshifts of a suitably large shift space.
These rather different settings are related by a Glasner-King type
correspondence: genericity in one is equivalent to genericity in the other.
By applying symbolic techniques in the shift-space model we derive new
results about genericity of dynamical properties for transitive and totally
transitive homeomorphisms of the Cantor set. We show that the isomorphism class
of the universal odometer is generic in the space of transitive systems. On the
other hand, the space of totally transitive systems displays much more varied
dynamics. In particular, we show that in this space the isomorphism class of
every Cantor system without periodic points is dense, and the following
properties are generic: minimality, zero entropy, disjointness from a fixed
totally transitive system, weak mixing, strong mixing, and minimal self
joinings. The last two stand in striking contrast to the situation in the
measure-preserving category. We also prove a correspondence between genericity
of dynamical properties in the measure-preserving category and genericity of
systems supporting an invariant measure with the same property.Comment: 48 pages, to appear in Ergodic Theory Dynamical Systems. v2: revised
exposition, added proof that the universal odometer is generic among
transitive Cantor homeomorphism
Impatience for Weakly Paretian Orders: Existence and Genericity
We study order theoretic and topological implications for impatience of weakly Paretian, representable orders on infinite utility streams. As a departure from the traditional literature, we do not make any continuity assumptions in proving the existence of impatient points. Impatience is robust in the sense that there are uncountably many impatient points. A general statement about genericity of impatience cannot be made for representable, weakly Paretian orders. This is shown by means of an example. If we assume a stronger sensitivity condition, then genericity obtains.Impatience Condition, Weak Pareto, Sensitivity Conditions, Genericity, Order Types, Uncountable Sets
On the semi-Riemannian bumpy metric theorem
We prove the semi-Riemannian bumpy metric theorem using equivariant
variational genericity. The theorem states that, on a given compact manifold
, the set of semi-Riemannian metrics that admit only nondegenerate closed
geodesics is generic relatively to the -topology, , in the
set of metrics of a given index on . A higher order genericity Riemannian
result of Klingenberg and Takens is extended to semi-Riemannian geometry.Comment: 17 page
Generic expansions of countable models
We compare two different notions of generic expansions of countable saturated
structures. One kind of genericity is related to model-companions and to
amalgamation constructions \'a la Hrushovski-Fra\"iss\'e. Another notion of
generic expansion is defined via topological properties and Baire category
theory. The second type of genericity was first formulated by Truss for
automorphisms. We work with a later generalization, due to Ivanov, to finite
tuples of predicates and functions
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