Saddle-focus singular cycles and prevalence of hyperbolicity
Saddles for expansive flows with the pseudo orbits tracing property
Let F be an expansive flow with the pseudo orbits tracing property on a compact metric space X. Suppose X is connected, locally connected and contains at least two distinct orbits. Then any point is a saddle.
Šarkovského věta a diferenciální rovnice
Šarkovského věta a diferenciální rovnice. II
Scattered homoclinics to a class of time-recurrent Hamiltonian systems
A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.
Sector estimates for Kleinian groups.
Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems
Using recent results on measure theory and algebraic geometry, we show how semidefinite programming can be used to construct invariant measures of one-dimensional discrete dynamical systems (iterated maps on a real interval). In particular we show that both discrete measures (corresponding to finite cycles) and continuous measures (corresponding to chaotic behavior) can be recovered using standard software.
Semigroup actions on tori and stationary measures on projective spaces
Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that the Γ-orbits...
Semigroup compactifications by generalized distal functions and a fixed point theorem.
Separation conditions on controlled Moran constructions
It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.
Separatrix conditions yielding either periodic orbits or unusual behavior for flows on M3.
Separatrix conditions yielding either periodic orbits or unusual behavior for flows on M3. (Short Communication).
Sequences of fixed point indices of iterations in dimension 2.
Sets of nondifferentiability for conjugacies between expanding interval maps
We study differentiability of topological conjugacies between expanding piecewise interval maps. If these conjugacies are not C¹, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the Lyapunov spectrum....
Shadowing and internal chain transitivity
The main result of this paper is that a map f: X → X which has shadowing and for which the space of ω-limits sets is closed in the Hausdorff topology has the property that a set A ⊆ X is an ω-limit set if and only if it is closed and internally chain transitive. Moreover, a map which has the property that every closed internally chain transitive set is an ω-limit set must also have the property that the space of ω-limit sets is closed. As consequences of this result, we show that interval maps with...
Shadowing in actions of some Abelian groups
We study shadowing properties of continuous actions of the groups and . Necessary and sufficient conditions are given under which a linear action of on has a Lipschitz shadowing property.
Shadowing in multi-dimensional shift spaces
We show that the class of expansive actions with P.O.T.P. is wider than the class of actions topologically hyperbolic in some direction . Our main tool is an extension of a result by Walters to the multi-dimensional symbolic dynamics case.
Shadowing lemma for family of -trajectories
Shape index and other indices of Conley type for local maps on locally compact Hausdorff spaces
We present a scheme for constructing various Conley indices for locally defined maps. In particular, we extend the shape index of Robbin and Salamon to the case of a locally defined map in a locally compact Hausdorff space. We compare the shape index with the cohomological Conley index for maps. We also prove the commutativity property of the Conley index, which is analogous to the commutativity property of the fixed point index.
Sharp determinants.