# Rare events for the Manneville–Pomeau map

@article{Freitas2015RareEF, title={Rare events for the Manneville–Pomeau map}, author={Ana Cristina Moreira Freitas and Jorge Milhazes Freitas and Mike Todd and Sandro Vaienti}, journal={Stochastic Processes and their Applications}, year={2015}, volume={126}, pages={3463-3479} }

## 28 Citations

### Dynamical counterexamples regarding the extremal index and the mean of the limiting cluster size distribution

- MathematicsJournal of the London Mathematical Society
- 2020

The extremal index (EI) is a parameter that measures the intensity of clustering of rare events and is usually equal to the reciprocal of the mean of the limiting cluster size distribution. We show…

### Dichotomy results for eventually always hitting time statistics and almost sure growth of extremes

- Mathematics
- 2021

Suppose (f,X , μ) is a measure preserving dynamical system and φ : X → R a measurable function. Consider the maximum process Mn := max{X1, . . . , Xn}, where Xi = φ ◦ f i−1 is a time series of…

### EXTREMAL DICHOTOMY FOR TORAL HYPERBOLIC AUTOMORPHISMS

- Mathematics
- 2016

Abstract. We consider the extreme value theory of a hyperbolic toral automorphism T : T2 ! T2 showing that, if a Hölder observation is a function of a Euclidean-type distance to a non-periodic point…

### Extremal dichotomy for uniformly hyperbolic systems

- Mathematics
- 2015

We consider the extreme value theory of a hyperbolic toral automorphism showing that, if a Hölder observation φ is a function of a Euclidean-type distance to a non-periodic point ζ and is strictly…

### Extreme Value Laws for Dynamical Systems with Countable Extremal Sets

- Mathematics
- 2016

We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is…

### Convergence of marked point processes of excesses for dynamical systems

- MathematicsJournal of the European Mathematical Society
- 2018

We consider stochastic processes arising from dynamical systems simply by evaluating an observable function along the orbits of the system and study marked point processes associated to extremal…

### Hitting Times and Positions in Rare Events

- MathematicsAnnales Henri Lebesgue
- 2022

We establish abstract limit theorems which provide sufficient conditions for a sequence $(A_{l})$ of rare events in an ergodic probability preserving dynamical system to exhibit Poisson asymptotics,…

### Entry and return times for semi-flows

- Mathematics
- 2017

Haydn, Lacroix and Vaienti (2005 Ann. Probab. 33 2043–50) proved that, for a given ergodic map, the entry time distribution converges in the small target limit, if and only if the corresponding…

### Hitting Times and Positions in Rare Events

- Mathematics
- 2018

— We establish abstract limit theorems which provide sufficient conditions for a sequence (Al) of rare events in an ergodic probability preserving dynamical system to exhibit Poisson asymptotics, and…

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