Entropy versus Volume for Pseudo-Anosovs
نویسندگان
چکیده
We discuss a comparison of the entropy of pseudo-Anosov maps and the volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both directions under some bounded geometry condition. Based on the experiments, we present various observations on the relation between minimal entropies and volumes, and on bounding constants for the entropy over the volume from below. We also provide explicit bounding constants for a punctured torus case.
منابع مشابه
Dynamics of the monodromies of the fibrations on the magic 3-manifold
We study the magic manifold N which is a hyperbolic and fibered 3-manifold. We give an explicit construction of a fiber Fa and its monodromy : Fa → Fa of the fibration associated to each fibered class a of N . Let δg (resp. δ + g ) be the minimal dilatation of pseudo-Anosovs (resp. pseudo-Anosovs with orientable invariant foliations) defined on an orientable closed surface of genus g. As a cons...
متن کاملA Homological Recipe for Pseudo-anosovs
We give a simple explicit construction of pseudo-Anosov mapping classes using an improvement of the homological criterion of Casson–Bleiler.
متن کاملL-cut splitting of translation surfaces and non-embedding of pseudo-Anosovs (in genus two)
We introduce a concept of a pair of parallel L-cuts on a translation surface, conjecture existence of such pairs for surfaces of genus g > 1, and find them for g = 2. We discuss applications to genus reducing decomposition of surfaces and to pseudo-Anosov maps (concerning their abelian-Nielsen equivalence classes and non-embedding into toral automorphisms). In particular, we provide a negative ...
متن کاملSmall dilatation pseudo-Anosovs and 3–manifolds
The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms φ : S → S, ranging over all surfaces S. More precisely, we consider pseudo-Anosovs φ : S → S with |χ(S)| log(λ(φ)) bounded above by some constant, and we prove that, after puncturing the surfaces at the singular points of the stable foliations, the resulting set of ma...
متن کاملA Note on Acylindrical Hyperbolicity of Mapping Class Groups
The aim of this note is to give the simplest possible proof that Mapping Class Groups of closed hyperbolic surfaces are acylindrically hyperbolic, and more specifically that their curve graphs are hyperbolic and that pseudo-Anosovs act on them as loxodromic WPDs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Experimental Mathematics
دوره 18 شماره
صفحات -
تاریخ انتشار 2009