Obtuse triangular billiards. I: Near the triangle.
Off-center reflections: caustics and chaos.
On a one-dimensional analogue of the Smale horseshoe
We construct a transformation T:[0,1] → [0,1] having the following properties: 1) (T,|·|) is completely mixing, where |·| is Lebesgue measure, 2) for every f∈ L¹ with ∫fdx = 1 and φ ∈ C[0,1] we have , where μ is the cylinder measure on the standard Cantor set, 3) if φ ∈ C[0,1] then for Lebesgue-a.e. x.
On a shadowing lemma in metric spaces
In the present paper conditions are studied, under which a pseudo-orbit of a continuous map , where is a metric space, is shadowed, in a more general sense, by an accurate orbit of the map .
On algebraic Anosov diffeomorphisms on nilmanifolds.
On almost specification and average shadowing properties
We study relations between the almost specification property, the asymptotic average shadowing property and the average shadowing property for dynamical systems on compact metric spaces. We show implications between these properties and relate them to other important notions such as shadowing, transitivity, invariant measures, etc. We provide examples showing that compactness is a necessary condition for these implications to hold. As a consequence, we also obtain a proof that limit shadowing in...
On analytic invariant measures for expanding mappings
On -closeness of invariant foliations under numerics.
On chaotic dynamics in rational polygonal billiards.
On connections, geodesics and sprays in synthetic differential geometry
On cusps and flat tops
Non-invertible Pesin theory is developed for a class of piecewise smooth interval maps which may have unbounded derivative, but satisfy a property analogous to . The critical points are not required to verify a non-flatness condition, so the results are applicable to maps with flat critical points. If the critical points are too flat, then no absolutely continuous invariant probability measure can exist. This generalises a result of Benedicks and Misiurewicz.
On evolution of small spheres in the phase space of a dynamical system*
We study the connection between the entropy of a dynamical system and the boundary distortion rate of regions in the phase space of the system.
On geometric detection of periodic solutions and chaotic dynamics.
On invariant measures for piecewise -transformations of the n-dimensional cube
On Irwin's proof of the pseudostable manifold theorem.
On maximal transitive sets of generic diffeomorphisms
On natural invariant measures on generalised iterated function systems.
On periodic orbits in discrete-time cascade systems.
On positively expansive differentiable maps
On quadratic symplectic mappings.