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pro vyhledávání: '"37E30"'
The sequence of Dold coefficients $(a_n(f))_n$ of a self-map $f\colon X \to X$ forms a dual sequence to the sequence of Lefschetz numbers $(L(f^n))_n$ of iterations of $f$ under the M\"obius inversion formula. The set ${\mathcal AP}(f) = \{ n \,\colo
Externí odkaz:
http://arxiv.org/abs/2411.19313
Autor:
Misiurewicz, M., Štimac, S.
We study the zero entropy locus for the Lozi maps. We first define a region $R$ in the parameter space and prove that for the parameters in $R$, the Lozi maps have the topological entropy zero. $R$ is contained in a larger region where every Lozi map
Externí odkaz:
http://arxiv.org/abs/2411.17836
We formulate and prove $\textit{a priori}$ bounds for the renormalization of H\'enon-like maps (under certain regularity assumptions). This provides a certain uniform control on the small-scale geometry of the dynamics, and ensures pre-compactness of
Externí odkaz:
http://arxiv.org/abs/2411.13624
We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any orbit (finite or infinite) in the phase space with a set of explicit i
Externí odkaz:
http://arxiv.org/abs/2411.13286
Autor:
Yang, Jonguk
We develop a renormalization theory of non-perturbative dissipative H\'enon-like maps with combinatorics of bounded type. The main novelty of our approach is the incorporation of Pesin theoretic ideas to the renormalization method, which enables us t
Externí odkaz:
http://arxiv.org/abs/2411.08317
Autor:
Morabito, Francesco
Given a compactly supported Hamiltonian diffeomorphism of the plane, one can define a generating function for it. In this paper, we show how generating functions retain information about the braid type of collections of fixed points of Hamiltonian di
Externí odkaz:
http://arxiv.org/abs/2410.06495
Autor:
Graff, Grzegorz, Topór, Patryk
We show that any sequence of integers satisfying necessary Dold's congruences is realized as the sequence of fixed point indices of the iterates of an orientation-reversing homeomorphism of $\mathbb{R}^{m}$ for $m\geq 3$. As an element of the constru
Externí odkaz:
http://arxiv.org/abs/2409.08753
A given self-map $f\colon M\to M$ of a compact manifold determines the sequence $\{L(f^n)\}_{n=1}^\infty$, of the Lefschetz numbers of its iterations. We consider its dual sequence $\{a_n(f)\}_{n=1}^\infty$ given by the M\"obius inversion formula. Th
Externí odkaz:
http://arxiv.org/abs/2408.12372
Autor:
Wiseman, Jim
We show that if an orientation-preserving homeomorphism of the plane has a topologically chain recurrent point, then it has a fixed point, generalizing the Brouwer plane translation theorem.
Externí odkaz:
http://arxiv.org/abs/2408.08183
Autor:
Anušić, Ana, Hoehn, Logan C.
We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding of the inve
Externí odkaz:
http://arxiv.org/abs/2407.16792