13 citations · 36 across the 14 of their papers we have counts for
15 papers
An inflated dynamic Laplacian to track the emergence and disappearance of semi-material coherent sets
Jason Atnip, Gary Froyland, Péter Koltai
Lagrangian methods continue to stand at the forefront of the analysis of time-dependent dynamical systems. Most Lagrangian methods have criteria that must be fulfilled by trajector…
Universal Gap Growth for Lyapunov Exponents of Perturbed Matrix Products
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We study the quantitative simplicity of the Lyapunov spectrum of -dimensional bounded matrix cocycles subjected to additive random perturbations. In dimensions 2 and 3, we estab…
Compound Poisson statistics for dynamical systems via spectral perturbation
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We consider random transformations where each map acts on a complete metrizable space . The randomness comes from an…
Thermodynamic Formalism and Perturbation Formulae for Quenched Random Open Dynamical Systems
Jason Atnip, Gary Froyland, Cecilia Gonzalez-Tokman +1
We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to…
Perturbation formulae for quenched random dynamics with applications to open systems and extreme value theory
Jason Atnip, Gary Froyland, Cecilia Gonzalez-Tokman +1
We consider quasi-compact linear operator cocycles driven by an invertible ergodic pr…
Equilibrium states for non-transitive random open and closed dynamical systems
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitiv…
Thermodynamic Formalism for Random Interval Maps with Holes
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to…
The Dynamics and Geometry of Semi-Hyperbolic Rational Semigroups
Jason Atnip, Hiroki Sumi, Mariusz Urbański
We study skew-product dynamics for a large class of finitely-generated semi--hyperbolic semigroups of rational maps acting on the Riemann sphere, which generalizes both the theory…
Thermodynamic Formalism for Random Weighted Covering Systems
Jason Atnip, Gary Froyland, Cecilia González-Tokman +1
We develop a quenched thermodynamic formalism for random dynamical systems generated by countably branched, piecewise-monotone mappings of the interval that satisfy a random coveri…
Extreme Value Theory with Spectral Techniques: application to a simple attractor
Jason Atnip, Nicolai Haydn, Sandro Vaienti
We give a brief account of application of extreme value theory in dynamical systems by using perturbation techniques associated to the transfer operator. We will apply it to the ba…
Quantization dimension for infinite conformal iterated function systems
Jason Atnip, Mrinal Kanti Roychowdhury, Mariusz Urbański
The quantization dimension function for an -conformal measure generated by an infinite conformal iterated function system satisfying the strong open set condition and by a…
Critically Finite Random Maps of an Interval
Jason Atnip, Mariusz Urbański
We consider random multimodal maps with negative Schwarzian derivative, defined on a finite union of closed intervals in , onto the interval with the base spac…
Dimensions of non-autonomous meromorphic functions of finite order
Jason Atnip
In this paper we study two classes of meromorphic functions previously studied by Mayer, Kotus, and Urbański. In particular we estimate a lower bound for the Julia set and the set…
Non-autonomous conformal graph directed Markov systems
Jason Atnip
In this paper we introduce and develop the theory of non-autonomous graph directed Markov systems which is a generalization of the theory of conformal graph directed Markov systems…
An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems
Jason Atnip
In this paper we deal with a large class of dynamical systems having a version of the spectral gap property. Our primary class of systems comes from random dynamics, but we also de…