Renormalization in Lorenz maps -- completely invariant sets and periodic orbits

Dynamical systems involving maps of the interval (37E05) Universality and renormalization of dynamical systems (37E20) Symmetries and invariants of dynamical systems (37C79)

Cites Work

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The $\beta$-transformation with a hole
Unique equilibrium states for flows and homeomorphisms with non-uniform structure
On the hyperbolicity of Lorenz renormalization
Topological and ergodic properties of symmetric sub-shifts
Renormalization and conjugacy of piecewise linear Lorenz maps
Matching for generalised $\beta$-transformations
Renormalization and $\alpha$-limit set for expanding Lorenz maps
The Lorenz attractor is mixing
Piecewise invertible dynamical systems
Periods and entropy for Lorenz-like maps
The structure of Lorenz attractors
The periodic points of renormalization
Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps
Mixing properties in expanding Lorenz maps
Continuity of the Hausdorff dimension for piecewise monotonic maps
Irregular sets, the $\beta$-transformation and the almost specification property
The classification of topologically expansive lorenz maps
Mixing properties of (α,β)-expansions
Topological conjugation of Lorenz maps by β-transformations
Periodic points for piecewise monotonic transformations
Symbolic dynamics for $\beta$-shifts and self-normal numbers
Farey–Lorenz Permutations for Interval Maps
Physical measures for infinitely renormalizable Lorenz maps
Matching in a family of piecewise affine maps
Entropy, topological transitivity, and dimensional properties of unique 𝑞-expansions
Critical itineraries of maps with constant slope and one discontinuity
Spike patterns and chaos in a map-based neuron model

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