We show that typical [in the sense of Bonatti and Viana (Ergod Theory Dyn Syst 24(5):1295–1330, 2004) and Avila and Viana (Port Math 64:311–376, 2007)] Hölder and fiber-bunched $$\text {GL}_d(\mathbb {R})$$ GL d ( R ) -valued cocycles over subshifts of finite type are uniformly quasi-multiplicative with respect to all singular value potentials. We prove the continuity of the singular value pressure and its corresponding (necessarily unique) equilibrium state for such cocycles, and apply this result to repellers. Moreover, we show that the pointwise Lyapunov spectrum is closed and convex, and establish partial multifractal analysis on the level sets of pointwise Lyapunov exponents for such cocycles.

中文翻译：

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典型共环的拟乘性

我们展示了典型的 [Bonatti 和 Viana (Ergod Theory Dyn Syst 24(5):1295–1330, 2004) 和 Avila and Viana (Port Math 64:311–376, 2007)] Hölder and fiber-bunched $ $\text {GL}_d(\mathbb {R})$$ GL d ( R ) - 有限类型子位移上的值余循环对于所有奇异值势是一致拟乘的。我们证明了这种共循环的奇异值压力及其相应（必然是唯一的）平衡状态的连续性，并将这一结果应用于排斥器。此外，我们证明了点式李雅普诺夫谱是封闭的和凸的，并建立了对此类共环的点式李雅普诺夫指数水平集的部分多重分形分析。