Sharpness for C¹ linearization of planar hyperbolic diffeomorphisms

2013/05/17 by Wenmeng Zhang, Zhang, Wenmeng, Weinian Zhang +1
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Analytic and geometric function theory #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1305.4122

Abstract

Planar hyperbolic diffeomorphisms can be referred to two cases: Poincaré domain (both eigenvalues lie inside the unit circle S¹) and Siegel domain (one eigenvalue inside S¹ but the other outside S¹). In Poincaré domain it was proved that C^1,α smoothness with α₀:=1-log|λ₂|/log|λ₁|0 is given, an interesting problem is: Is the exponent α₀ also sharp? On the other hand, in Siegel domain we only know that C^1,α smoothness with α∈ (0,1] admits C¹ linearization. In this paper we further study the sharpness for C¹ linearization in both cases.

Citations

• Analytic extensions of differentiable functions defined in closed sets

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