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1.
Letf a a∈A be a C2 one-parameter family of non-flat unimodal maps of an interval into itself anda* a parameter value such that
- fa* satisfies the Misiurewicz Condition,
- fa* satisfies a backward Collet-Eckmann-like condition,
- the partial derivatives with respect tox anda of f a n (x), respectively at the critical value and ata*, are comparable for largen.
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Let X be a compact connected subset of d with non-empty interior,and T:X X a real analytic full branch expanding map with countablymany branches. Elements of a thermodynamic formalism for suchsystems are developed, including criteria for compactness oftransfer operators acting on spaces of bounded holomorphic functions.In particular, a new sufficient condition for the existenceof a T-invariant probability measure equivalent to Lebesguemeasure is obtained. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2345-2353
In this paper we provide a closed mathematical formulation of our previous results in the field of symbolic dynamics of unimodal maps. This being the case, we discuss the classical theory of applied symbolic dynamics for unimodal maps and its reinterpretation using Gray codes. This connection was previously emphasized but no explicit mathematical proof was provided. The work described in this paper not only contributes to the integration of the different interpretations of symbolic dynamics of unimodal maps, it also points out some inaccuracies that exist in previous works. 相似文献
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We consider a class of generalized Fibonacci unimodal maps for which the central return times {s_n} satisfy that s_n = s_(n-1) +ks_(n-2) for some k ≥ 1. We show that such a unimodal map admits a unique absolutely continuous invariant probability with exactly stretched exponential decay of correlations if its critical order lies in(1, k+1). 相似文献
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《Mathematische Nachrichten》2017,290(2-3):382-392
In this paper, we study the topology of real analytic map‐germs with isolated critical value , with . We compare the topology of f with the topology of the compositions , where are the projections , for . As a main result, we give necessary and sufficient conditions for f to have a Lê–Milnor fibration in the tube. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(9):3119-3127
In this paper we introduce an algorithm which allows us to compute the topological entropy of a class of piecewise monotone continuous interval maps. The algorithm can be applied to a class of economic models called duopolies, and it can be useful to compute the topological entropy of periodic sequences of continuous maps which have been used in some population growth models. 相似文献
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Zeng Fanping 《数学学报(英文版)》1998,14(4):457-462
LetP andAC be two primary sequences with min{P, AC}≥RLR
∞,ρ(P) and ρ(AC) be the eigenvalues ofP andAC, respectively. Letf∈C
0
(I, I) be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved thatf has the kneading sequenceK(f)≥(RC)
*m
*P if λ≥(ρ(P))1/2m, andK(f)>(RC)
*m*AC*E for any shift maximal sequenceE if λ>(ρ(AC))1/2m. The value of (ρ(P))1/2m or (ρ(AC))1/2m is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.
Project supported by the National Natural Science Foundation of China 相似文献
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Yoram Sagher 《Israel Journal of Mathematics》1969,7(4):350-356
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Journal of Algebraic Combinatorics - In this paper, we consider the possible types of regular maps of order $$2^n$$ , where the order of a regular map is the order of automorphism group of the map.... 相似文献
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M. Belliart 《Commentarii Mathematici Helvetici》2002,77(3):524-548
Let M be a closed connected real analytic manifold; let be a free group on two generators. The set of analytic actions of on M endowed with Taken‚s topology contains a nonempty open subset whose corresponding actions share three properties: (a) they
have every orbit dense, (b) they leave invariant no geometric structure on M, (c) any homeomorphism conjugating two of them is analytic.
Received: October 3, 2001 相似文献
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Let τ1 and τ2 be unimodal maps of the interval [0,1]. Let ψ be a topological conjugacy between τ1 and τ2. Sufficient conditions are given which guarantee that ψ is singular.
This research was supported by NSERC Grants and an FCAC grant from the Quebec government. 相似文献
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Ta Thi Hoai An 《Indagationes Mathematicae》2008,19(3):481-492
We prove non-Archimedean analogs of results of Noguchi and Winkelmann showing algebraic degeneracy of rigid analytic maps to projective varieties omitting an effective divisor with sufficiently many irreducible components relative to the rank of the group they generate in the Néron-Severi group of the variety. 相似文献
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Let be an analytic ring. We show: (1) has finite Pythagoras number if and only if its real dimension is , and (2) if every positive semidefinite element of is a sum of squares, then is real and has real dimension .