共查询到20条相似文献,搜索用时 31 毫秒
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Aleksander Czechowski Robert Vandervorst 《Journal of Fixed Point Theory and Applications》2017,19(1):231-262
Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of \({\mathbb {D}^{2}}\), allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition, we utilize the Conley index theory of discrete braid classes as introduced in Ghrist et al. (Invent. Math. 152:369–432, 2003) and Ghrist et al. (C. R. Acad. Sci. Paris Sér. I Math. 331:861–865, 2000) to obtain a Morse type forcing theory of periodic points: a priori information about periodic points determines a mapping class which may force additional periodic points. 相似文献
3.
夏红强 《数学物理学报(B辑英文版)》2010,30(3):701-712
We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O(1/√n). 相似文献
4.
Yu. S. Ilyashenko 《Functional Analysis and Its Applications》2008,42(4):298-307
We construct a diffeomorphism F of a manifold with boundary into itself with the following property. The attractor of F has two components, and the attracting basins of these components are dense in the phase space and have positive measure. We prove that the class of examples constructed in the paper has codimension infinity in the space of all diffeomorphisms of the same manifold. 相似文献
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C. Bonatti V. Z. Grines V. S. Medvedev O. V. Pochinka 《Proceedings of the Steklov Institute of Mathematics》2007,256(1):47-61
We study bifurcations of Morse-Smale diffeomorphisms under a change of the embedding of the separatrices of saddle periodic points in the ambient 3-manifold. The results obtained are based on the following statement proved in this paper: for the 3-sphere, the space of diffeomorphisms of North Pole-South Pole type endowed with the C 1 topology is connected. This statement is shown to be false in dimension 6. 相似文献
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Javier Ribón 《Bulletin of the Brazilian Mathematical Society》2012,43(2):247-283
We study the formal conjugacy properties of germs of complex analytic diffeomorphisms defined in the neighborhood of the origin of ? n . More precisely, we are interested in the nature of formal conjugations along the fixed points set. We prove that there are formally conjugated local diffeomorphisms ??, ?? such that every formal conjugation $\hat \sigma$ (i.e. $\eta \circ \hat \sigma = \hat \sigma \circ \phi$ ) does not extend to the fixed points set Fix(??) of ??, meaning that it is not transversally formal (or semi-convergent) along Fix(??). We focus on unfoldings of 1-dimensional tangent to the identity diffeomorphisms. We identify the geometrical configurations preventing formal conjugations to extend to the fixed points set: roughly speaking, either the unperturbed fiber is singular or generic fibers contain multiple fixed points. 相似文献
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We consider the class G 4 of Morse—Smale diffeomorphisms on $ \mathbb{S} $ 3 with nonwandering set consisting of four fixed points (namely, one saddle, two sinks, and one source). According to Pixton, this class contains a diffeomorphism that does not have an energy function, i.e., a Lyapunov function whose set of critical points coincides with the set of periodic points of the diffeomorphism itself. We define a quasi-energy function for any Morse—Smale diffeomorphism as a Lyapunov function with the least number of critical points. Next, we single out the class G 4,1 ? G 4 of diffeomorphisms inducing a special Heegaard splitting of genus 1 of the sphere $ \mathbb{S} $ 3. For each diffeomorphism in G 4,1, we present a quasi-energy function with six critical points. 相似文献
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We study the algebraic structure of several groups of differentiable diffeomorphisms in . We show that any given sufficiently smooth diffeomorphism can be written as the composition of a finite number of diffeomorphisms which are symmetric under reflection, essentially one-dimensional and about as differentiable as the given one.
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Tomasz Rybicki 《Geometriae Dedicata》1997,67(2):181-186
We introduce a notion of pseudo-n- transitivity which is a nontransitive counterpart of the n-transitivity. The main result states that any group of diffeomorphisms which satisfies the locality condition is pseudo-n-transitive for each n 1. 相似文献
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We compute the Hofer distance for a certain class of compactly supported symplectic diffeomorphisms of 2n. They are mainly characterized by the condition that they can be generated by a Hamiltonian flow
H
t
which possesses only constantT-periodic solutions for 0 <T 1. In addition, we show that on this class Hofer's and Viterbo's distances coincide. 相似文献
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Ch. Bonatti L. J. Díaz F. Vuillemin 《Bulletin of the Brazilian Mathematical Society》1998,29(1):99-144
We show that the loss of hyperbolicity of an Anosov diffeomorphism of the torusT
2 can be produced by a cubic tangency at a heteroclinic point. Such a first bifurcation is generic for 3-parameters families of diffeomorphisms. Our construction may also be applied to any basic set of a surface diffeomorphism. Moreover, if the pointq of cubic tangency corresponds to a lateral point of then the bifurcation is generic for two parameters. In this case the pointq may be a homoclinic intersection.Dedicated to the memory of R. MañéPartially supported by CNPq (Brazil) and CNRS (France).Supported by CNRS (France), Rectorat Université de Bourgogne (France) and CNPq (Brazil). 相似文献
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M. V. Losik 《Geometriae Dedicata》2001,88(1-3):21-36
A structure of the group of diffeomorphisms for the orbit space of an orthogonal representation G>
O(V) of a compact Lie group G is studied. For a finite G, it is proved that each diffeomorphism of the orbit space V/G has a smooth lift to V and the component group of the group of Diff(V/G is described, especially in the case when G is a finite Coxeter group. Similar results are obtained for the isotropy representations of some symmetric spaces. 相似文献
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Sergiy Maksymenko 《Central European Journal of Mathematics》2009,7(2):272-298
Let F be a C
∞ vector field defined near the origin O ∈ ℝ
n
, F(O) = 0, and (F
t
) be its local flow. Denote by
the set of germs of orbit preserving diffeomorphisms h: ℝ
n
→ ℝ
n
at O, and let
, (r ≥ 0), be the identity component of
with respect to the weak Whitney W
r
topology. Then
contains a subset
consisting of maps of the form F
α(x)(x), where α: ℝ
n
→ ℝ runs over the space of all smooth germs at O. It was proved earlier by the author that if F is a linear vector field, then
=
.
In this paper we present a class of examples of vector fields with degenerate singularities at O for which
formally coincides with
, i.e. on the level of ∞-jets at O.
We also establish parameter rigidity of linear vector fields and “reduced” Hamiltonian vector fields of real homogeneous polynomials
in two variables.
相似文献
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We give a characterization of structurally stable diffeomorphisms by making use of the notion of L
p
-shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C
1-interior of the set of diffeomorphisms having L
p
-shadowing property. 相似文献
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Albert Fathi 《Inventiones Mathematicae》1987,87(1):129-151
Summary We show that it is possible to obtain many pseudo-Anosov diffeomorphisms from Dehn twists. In particular, we generalize a theorem of Long and Morton to obtain that iff is a pseudo-Anosov diffeomorphism of an oriented surface andT
is the Dehn twist around the simple closed curve , then the isotopy class ofT
n
f contains a pseudo-Anosov diffeomorphism except for at most 7 consecutive values ofn. 相似文献
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Todd R. Young 《Proceedings of the American Mathematical Society》1997,125(7):1987-1995
It is shown that the set of heteroclinic orbits between two periodic orbits of saddle-node type induces functional moduli which are completely contained in a new `transition map'. For one-dimensional diffeomorphisms with saddle-node periodic points, two such diffeomorphisms are conjugated if and only if the transition maps of their heteroclinic orbits are the same. An equivalent transition map is given for diffeomorphisms with hyperbolic periodic points, and it is shown that this transition map is an invariant of conjugation. However, in this case the transition map alone is sufficient to guarantee conjugacy only in a limited sense.
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Nobuya Watanabe 《Geometric And Functional Analysis》2007,17(1):320-331
We obtain results on the growth sequences of the differential for iterations of circle diffeomorphisms without periodic points.
Received: June 2005 Revision: December 2005 Accepted: February 2006 相似文献