29 citations · 151 across the 52 of their papers we have counts for
55 papers
Continuous Lebesgue measure-preserving maps on one-dimensional manifolds: a survey
Jozef Bobok, Jernej Činč, Piotr Oprocha +1
We survey the current state-of-the-art about the dynamical behavior of continuous Lebesgue measure-preserving maps on one-dimensional manifolds.
The horizontal chord set: to CIRM and back
Diana Davis, Serge Troubetzkoy
We study the set of lengths of the horizontal chords of a continuous function. We give a new proof of Hopf's characterization of this set, and show that it implies that no matter w…
Are generic dynamical properties stable under composition with rotations?
Jozef Bobok, Jernej Činč, Piotr Oprocha +1
In this paper we provide a detailed topological and measure-theoretic study of Lebesgue measure-preserving circle maps that are rotated with inner and outer rotations which are ind…
An upper bound on topological entropy of the Bunimovich stadium billiard map
Jernej Činč, Serge Troubetzkoy
We show that the topological entropy of the billiard map in a Bunimovich stadium is at most log(3.49066).
Vertex to vertex geodesics on platonic solids
Serge Troubetzkoy
We give a simple proof based on symmetries that there are no geodesics from a vertex to itself in the cube, tetrahedron, octahedron, and icosahedron.
Periodic points and shadowing property for generic Lebesgue measure preserving interval maps
Jernej Činč, Jozef Bobok, Piotr Oprocha +1
We show that for the generic continuous maps of the interval and circle which preserve the Lebesgue measure it holds for each k 1 that the set of periodic points of period k…