11 citations · 11 across the 5 of their papers we have counts for
5 papers · 1 filter
Pair correlation statistics for dynamical systems
Simon Baker, Mike Todd
We study the pair correlation statistics of orbits generated by maps on the interval. We show that under suitable mixing and multifractal assumptions, the pair correlation statisti…
Almost sure orbits closeness
Maxim Kirsebom, Philipp Kunde, Tomas Persson +1
We consider the minimal distance between orbits of measure preserving dynamical systems. In the spirit of dynamical shrinking target problems we identify distance rates for which a…
Convergence of the Birkhoff spectrum for nonintegrable observables
Godofredo Iommi, Mike Todd, Boyuan Zhao
We consider interval maps with countably many full branches and observables with polynomial tails. We show that the Birkhoff spectrum is real analytic and that its convergence to t…
A functional limit theorem for a dynamical system with an observable maximised on a Cantor set
Raquel Couto, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas +1
We consider heavy-tailed observables maximised on a dynamically defined Cantor set and prove convergence of the associated point processes as well as functional limit theorems. The…
Equilibrium states for interval maps: the potential
Henk Bruin, Mike Todd
Let be a multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium state…