80 citations · 127 across the 7 of their papers we have counts for
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A dynamical approach to validated numerics
Oliver Jenkinson, Mark Pollicott
We describe a method, using periodic points and determinants, for giving alternative expressions for dynamical quantities (including Lyapunov exponents and Hausdorff dimension of i…
How many inflections are there in the Lyapunov spectrum?
Oliver Jenkinson, Mark Pollicott, Polina Vytnova
Iommi & Kiwi showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this pape…
Ergodic optimization in dynamical systems
Oliver Jenkinson
Ergodic optimization is the study of problems relating to maximizing orbits, maximizing invariant measures and maximum ergodic averages. An orbit of a dynamical system is called f-…
Rigorous effective bounds on the Hausdorff dimension of continued fraction Cantor sets: a hundred decimal digits for the dimension of
Oliver Jenkinson, Mark Pollicott
We prove that the algorithm of [13] for approximating the Hausdorff dimension of dynamically defined Cantor sets, using periodic points of the underlying dynamical system, can be u…
Joint spectral radius, Sturmian measures, and the finiteness conjecture
Oliver Jenkinson, Mark Pollicott
The joint spectral radius of a pair of 2x2 real matrices is defined to be $r(A_0,A_1)= \limsup_{n\to\infty} \max \{\|A_{i_1}...A_{i_n}\|^{1/n}: i_j…
Explicit eigenvalue estimates for transfer operators
Oscar F. Bandtlow, Oliver Jenkinson
We consider transfer operators acting on spaces of holomorphic functions, and provide explicit bounds for their eigenvalues. More precisely, if D is any open set in C^d, and L is a…