# Effective high-temperature estimates for intermittent maps

## TL;DR

This paper establishes spectral gaps for transfer operators of intermittent maps in high-temperature regimes using perturbation theory, enabling broader application of thermodynamic formalism results.

## Contribution

It introduces a method to prove spectral gaps for transfer operators of intermittent maps under high-temperature conditions, extending previous results to more general potentials.

## Key findings

- Spectral gap for Pommeau-Manneville maps with Lipschitz constant < 0.0014.
- Spectral gap for 2-to-1 unimodal maps with total variation < 0.0069.
- Classical spectral gap definition coincides with the stronger one, enabling application of thermodynamic results.

## Abstract

Using quantitative perturbation theory for linear operators, we prove spectral gap for transfer operators of various families of intermittent maps with almost constant potentials ("high-temperature" regime). H\"older and bounded p-variation potentials are treated, in each case under a suitable assumption on the map, but the method should apply more generally. It is notably proved that for any Pommeau-Manneville map, any potential with Lispchitz constant less than 0.0014 has a transfer operator acting on Lip([0, 1]) with a spectral gap; and that for any 2-to-1 unimodal map, any potential with total variation less than 0.0069 has a transfer operator acting on BV([0, 1]) with a spectral gap. We also prove under quite general hypotheses that the classical definition of spectral gap coincides with the formally stronger one used in (Giulietti et al. 2015), allowing all results there to be applied under the high temperature bounds proved here: analyticity of pressure and equilibrium states, central limit theorem, etc.