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1.
A class of uniformly expanding, piecewise C
2-diffeomorphisms from domains IR
d
(bounded or not) into themselves is considered. It is shown that the number of the extreme points of Fix ( P
)={gG:P g=g} where P
is the Frobenius-Perron operator associated with and G={gL
1: g0 g=1}, can be determined in an effective way. Moreover, it is shown that the sequence { P
j
g} is convergent in L
1 for any gG, and in the topology of uniform convergence for any gG(1). The limit is a linear projection R in L
1 (defined by (3.1)) which maps G onto Fix ( P
) (see Th. 3.1).Dedicated to professor A. Lasota on the occasion of his 60th birthday 相似文献
2.
In this paper, we construct an example of a C
1 expanding map of the circle which preserves Lebesgue measure such that the system is ergodic, but not weak-mixing. This contrasts
with the case of C
1+ε maps, where any such map preserving Lebesgue measure has a Bernoulli natural extension and hence is weak-mixing. 相似文献
3.
We prove that the chain-transitive sets of C 1-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes
are dense among the chain-recurrence classes.
This result is a consequence of a global connecting lemma, which allows to build by a C 1-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C 1-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff topology by a finite segment of a genuine orbit.
As a consequence, we obtain a criterion for proving the tolerance stability conjecture in Diff 1(M). 相似文献
7.
This paper was written while the first three authors were visiting the University of Dortmund in 1992. The first two authors thankfully acknowledge the support offered by TEMPUS and the University of Dortmund. 相似文献
9.
Some piecewise C
2-diffeomorphisms which expand distances uniformly (in all directions) are considered. It is shown that they have the so-called Bernoulli property, i.e. their natural extensions are isomorphic to Bernoulli shifts. 相似文献
11.
We show that a hyperbolic punctured torus bundle admits a foliation by lines which is covered by a product foliation. Thus its fundamental group acts freely on the plane. 相似文献
14.
Recently, Mok and Zhang (2019) introduced the notion of admissible pairs (X0, X) of rational homogeneous spaces of Picard number 1 and proved rigidity of admissible pairs (X0, X) of the subdiagram type whenever X0 is nonlinear. It remains unsolved whether rigidity holds when (X0, X) is an admissible pair NOT of the subdiagram type of nonlinear irreducible Hermitian symmetric spaces such that (X0, X) is nondegenerate for substructures. In this article we provide sufficient conditions for confirming rigidity of such an admissible pair. In a nutshell our solution consists of an enhancement of the method of propagation of sub-VMRT (varieties of minimal rational tangents) structures along chains of minimal rational curves as is already implemented in the proof of the Thickening Lemma of Mok and Zhang (2019). There it was proven that, for a sub-VMRT structure \(\overline{\omega} : \mathscr{C}(S) \rightarrow S\) on a uniruled projective manifold \((X,\,{\cal K})\) equipped with a minimal rational component and satisfying certain conditions so that in particular S is “uniruled” by open subsets of certain minimal rational curves on X, for a “good” minimal rational curve ? emanating from a general point x ∈ S, there exists an immersed neighborhood N? of ? which is in some sense “uniruled” by minimal rational curves. By means of the Algebraicity Theorem of Mok and Zhang (2019), S can be completed to a projective subvariety Z ? X. By the author’s solution of the Recognition Problem for irreducible Hermitian symmetric spaces of rank ? 2 (2008) and under Condition (F), which symbolizes the fitting of sub-VMRTs into VMRTs, we further prove that Z is the image under a holomorphic immersion of X0 into X which induces an isomorphism on second homology groups. By studying ?*-actions we prove that Z can be deformed via a one-parameter family of automorphisms to converge to X0 ? X. Under the additional hypothesis that all holomorphic sections in Γ(X0, Tx∣x0) lift to global holomorphic vector fields on X, we prove that the admissible pair (X0, X) is rigid. As examples we check that (X0, X) is rigid when X is the Grassmannian G(n, n) of n-dimensional complex vector subspaces of W ? ?2n, n ? 3, and when X0 ? X is the La grangian Grassmannian consisting of Lagrangian vector subspaces of (W, σ) where σ is an arbitrary symplectic form on W. 相似文献
15.
In the ongoing revision of the classification of the finite simple groups there is a subdivision into two classes of groups, which reflects whether semisimple elements or unipotent elements are the primary focus of the investigation. While semisimple methods naturally lead to the definition of groups of even type, unipotent methods, notably the amalgam method, naturally lead to groups of even characteristic. This paper clarifies the relationship between the two definitions and thus makes the amalgam method available for use in the classification of groups of even type. 相似文献
18.
We give sufficient (and necessary) conditions of local character ensuring that a geometric graph is the 1-skeleton of an unstacked triangulation of a simple polygon. 相似文献
20.
We prove that each structurally stable diffeomorphism f on a closed 3-manifold M 3 with a two-dimensional surface nonwandering set is topologically conjugated to some model dynamically coherent diffeomorphism. 相似文献
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