# Questions tagged [thermodynamic-formalism]

Thermodynamic formalism is the study of equilibrium states, Gibbs measures and topological pressure for dynamical systems.

10 questions
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### Equation of state for hard rods

Some context: For ideal gases, the thermodynamic equation of state is the well-known: $$pV = nRT \tag{1}$$ where $n$ is the amount of substance, $R$ the universal gas constant and $P,V,T$ are ...
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### Can a smooth diffeomorphisms of a Riemannian manifold have only positive Lyapunov exponents?

Let $\mu$ be some ergodic measure of our compact Riemannian manifold $M$, which is preserved by $f\in Diff^{1+\beta}(M)$. Is it possible that all the Lyapunov exponents of $\mu$ will be positive? ...
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Consider the classical Multifractal Analysis, and the decomposition of the state space $X$ into level sets $$X=\bigcup_{\alpha}\left\{x\mid d_\mu(x)=\alpha\right\}\cup\left\{x\mid d_\mu(x) \,\mathrm{... 1answer 193 views ### Estimates of Hausdorff dimension (and its derivatives) For example, the cookie cutter maps, say T:I_1 \cup I_2 \subset [0,1] \to [0,1]  is a C^2 map such that |T'|>1 and provided I_1 and I_2 are disjoint closed intervals and T(I_i)=[0,1]. ... 0answers 117 views ### Is \text{Bow}(X,T) a Banach Space? Let X=\{0,1\}^{\mathbb{N}} be the sequence space and T:X\to X the left shift mapping. Define the vector space \text{Bow}(X,T) as$$ \text{Bow}(X,T)=\{f\in C^{0}(X);~\sup_{n\in \mathbb{N}}\sup_{...
I am interested in recognising graphs (or matrices, or subshifts of finite type) using topological pressure. Suppose that we play the following game: ${\bf Step 1:}$ I write down an irreducible n x n ...