Expanding thurston maps

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August undefined, 2024

WebJan 31, 2024 · Bonk M., Meyer D.: Expanding Thurston Maps, volume 225 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI … WebA Thurston map is a branched covering map on a two-dimensional topological sphere such that each critical point of the map has a finite orbit under iteration. It is called expanding if, roughly speaking, preimages of …

Unmating of expanding Thurston maps with Julia set …

WebExpanding Thurston maps give natural topological models for investigating the dynamical and geo-metric properties of (non-uniformly expanding) postcritically-ﬁnite rational maps. On the other hand, an expanding Thurston map may be obstructed, i.e., not topologically conjugate to a rational map, in Webﬁnite are Thurston maps. The Thurston maps we will focus on are rational maps with no periodic critical points. Such rational maps have Julia set equal to Ĉ, and are also expanding on S2 as described in [1]: Deﬁnition 2.2. Suppose that f is a Thurston map with critical set post:= post(f), and that C ⊆ S2 is a Jordan curve containing post ... leeds school of communication

Thermodynamic Formalism for Coarse Expanding Dynamical Systems

WebApr 6, 2024 · A Thurston map is called expanding, if, roughly speaking, preimages of a fine open cover of the underlying sphere under iterates of the map become finer and … WebMar 1, 2024 · Expanding Thurston maps form a class of branched covering maps on the topological -sphere which are topological models of some non-uniformly expanding … WebThurston map f is expanding (see (2.3) for the precise deﬁnition). Theorem1.2 Let f: S2 → S2 be an expanding Thurston map. Then, the following conditions are equivalent: (i) f is the quotient of a torus endomorphism. (ii) f has a parabolic orbifold. (iii) f is a Lattès-type map. Since every quotient f of a torus endomorphism is actually a ... leeds school of law

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WebJan 31, 2024 · In this paper, we use the thermodynamical formalism to show that there exists a unique equilibrium state $${\\mu_\\phi}$$ μ ϕ for each expanding Thurston map $${f : S^2\\rightarrow S^2}$$ f : S 2 → S 2 together with a real-valued Hölder continuous potential $${\\phi}$$ ϕ . Here the sphere S2 is equipped with a natural metric induced by … WebFind many great new & used options and get the best deals for Ergodic Theory of Expanding Thurston Maps by Zhiqiang Li (English) Hardcover Boo at the best online prices at eBay! Free shipping for many products! leeds school of chemistryWebThis monograph is devoted to the study of the dynamics of expanding Thurston maps under iteration. A Thurston map is a branched covering map on a two-dimensional topological sphere such that each ... leeds schools october half term 2022

"WebIt is also clear that iff, g, hare Thurston maps,f is (Thurston) equivalent to g, and gis equivalent toh, then f is equivalent toh. Thus, Thurston equivalence leads to a notion of equivalence for Thurston maps. If two Thurston mapsfandgare equivalent, then for eachn ∈ Nthe iteratesfn andgn are also equivalent. To show this statement, one ... " - Expanding thurston maps

Expanding thurston maps

WebThe study in the setting of expanding Thurston maps is ongoing. Jie Ji has been studying invariant graphs on the plane under the supervision of J. Rivera-Letelier and me. Xiaoran … WebSep 19, 2010 · Expanding Thurston maps as quotients Daniel Meyer Mathematics 2009 A Thurston map is a branched covering map $f\colon S^2\to S^2$ that is postcritically …

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WebFeb 4, 2011 · One fundamental theorem in the theory of holomorphic dynamics is Thurston's topological characterization of postcritically finite rational maps. Its proof is a beautiful application of Teichmuller theory. In this chapter we provide a self-contained proof of a slightly generalized version of Thurston's theorem (the marked Thurston's … WebExpanding Thurston Maps: What Are They and Why Do They Matter? Expanding Thurston Maps are maps that look like the following rational maps: z7! 4z(z 1)(z+ 1) (z …

Webmap is parabolic, and the cardinality of the postcritical set can only be 3 or 4. Latt`es maps with #post(f) = 4 are also referred to as ﬂexible Latt`es maps. The notion of an expanding Thurston map was introduced in [3] as a topological analog of a postcritically ﬁnite rational map whose Julia set is the whole sphere Cb. WebNov 5, 2015 · We say that a Thurston map is expanding if for any two points x,y∈S2, their preimages under iterations of the map gets closer and closer. See Definition 3.4for a …

WebWe also assume that the maps are expanding in a suitable sense. Every expanding Thurston map is a factor of a shift operator. This link to symbolic dynamics suggests our … http://amj.math.stonybrook.edu/pdf-Springer-final/020-0156.pdf

WebApr 7, 2024 · Section 6.3 consists of the proof of Theorem 6.1 in the form of three separate theorems. Namely, we show in Theorem 6.10 the asymptotic h-expansiveness of expanding Thurston maps without periodic critical points.The proof relies on a quantitative upper bound of the frequency for an orbit under such a map to get close to the set of …

WebSep 14, 2024 · In general, the converse implication is not true, but our main result provides such a converse under the assumption that the Thurston map f is expanding (see for the precise definition). Theorem 1.2. Let $f: S^2\rightarrow S^2$ be an expanding Thurston map. Then, the following conditions are equivalent: (i) leeds senior bus passWebNov 28, 2024 · A Thurston map is a branched covering map on a two-dimensional topological sphere such that each critical point of the map has a finite orbit under … leeds sen team contactWebSep 15, 2002 · On the Aubry–Mather theory for symbolic dynamics. E. Garibaldi, A. Lopes. Mathematics. Ergodic Theory and Dynamical Systems. 2008. Abstract We propose a new model of ergodic optimization for expanding dynamical systems: the holonomic setting. In fact, we introduce an extension of the standard model used in this theory. leed ss creditWebSep 3, 2011 · Consider a rational map f of degree at least 2 acting on its Julia set J(f), a Hölder continuous potential φ: J(f) → ℝ and the pressure P(f,φ). In the case where $$\\mathop {\\sup }\\limits_{J(f)} \\phi < P(f,\\phi ),$$ the uniqueness and stochastic properties of the corresponding equilibrium states have been extensively studied. In this … leeds send local offerWebApr 10, 2024 · In a series of papers [18,19,20,21], Li works out the thermodynamic formalism for expanding Thurston maps, with respect to the visual metric. In a similar vein, Haïssinsky–Pilgrim [ 15 ] define more generally the concept of coarse expanding conformal (cxc) system, developing in an axiomatic way the notion of expansion for maps of … leeds selective licence registerWebAbout this Series. The series 'Atlantis Studies in Dynamical Systems' publishes monographs in the area of Dynamical Systems, written by leading experts in the field and useful for both students and researchers.Books with a theoretical nature will be published alongside books emphasizing applications. Volumes in this Series leedssexualhealth.comWebMar 1, 2024 · Ground states and periodic orbits for expanding Thurston maps. Expanding Thurston maps form a class of branched covering maps on the topological -sphere which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption initially investigated by W. P. Thurston, M. … how to factory reset lenovo flex 3 from usb