# Renormalization for unimodal maps with non-integer exponents

## TL;DR

This paper develops an analytic framework for renormalization of unimodal maps with arbitrary critical exponents and proves hyperbolicity for maps with exponents near even integers, advancing understanding of their dynamical behavior.

## Contribution

It introduces a new analytic setting for renormalization of unimodal maps with non-integer exponents and proves hyperbolicity in a specific parameter regime, extending prior results.

## Key findings

- Established hyperbolicity of renormalization for maps with critical exponents close to even integers
- Developed an analytic framework applicable to non-integer critical exponents
- Extended the scope of renormalization theory in dynamical systems

## Abstract

We define an analytic setting for renormalization of unimodal maps with an arbitrary critical exponent. We prove the global Hyperbolicity of Renormalization conjecture for unimodal maps of bounded type with a critical exponent which is sufficiently close to an even integer.