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Vanderlei Horita

Publications and source records attributed to Vanderlei Horita.

7 recordsLinked to original sources
arXiv2026

Continuity of Hausdorff Dimension at Hopf Bifurcation

We investigate the continuity of Hausdorff dimension and box dimension (limit capacity) of non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomophisms through a Hopf bifurcation studied by Horita and Viana (see Discret. Contin. Dyn. Syst., 13 (2005), 1125-1137). Here, we extend their work showing that both dimensions are continuous at paremeter bifurcation. In the proof, we consider maps with holes introduced by Horita and Viana in Journal of Statistical Physics 105(2001), 835-862 and further developed by Dysman in Journal of Statistical Physics 120(2005),479-509, relating the Hausdorff dimension with the volume of the hole.

math.DS↗
arXiv2023

Building Expansion for Generalizations of Viana Maps

In a seminal paper, Viana built examples of maps presenting two positive Lyapunov exponents exploring skew-products of a (uniformly) expanding map and a quadratic map (order 2 critical point) perturbed by some level of noise. Here we extend that construction replacing the quadratic underlying dynamics by maps with a more degenerated critical point.

math.DS↗
arXiv2016

Stable Ergodicity and Accessibility for certain Partially Hyperbolic Diffeomorphisms with Bidimensional Center Leaves

We consider classes of partially hyperbolic diffeomorphism $f:M\to M$ with splitting $TM=E^s\oplus E^c\oplus E^u$ and $\dim E^c=2$. These classes include for instance (perturbations of) the product of Anosov and conservative surface diffeomorphisms, skew products of surface diffeomorphisms over Anosov, partially hyperbolic symplectomorphisms on manifolds of dimension four with bidimensional center foliation whose center leaves are all compact. We prove that accessibility holds in these classes for $C^1$ open and $C^r$ dense subsets and moreover they are stably ergodic.

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arXiv2016

$C1$-Genericity of Symplectic Diffeomorphisms and Lower Bounds for Topological Entropy

There is a $C^1$-residual (Baire second class) subset $\mathcal{R}$ of symplectic diffeomorphisms on $2d$-dimensional manifold, $d\geq 1$, such that for every non-Anosov $f$ in $\mathcal{R}$ its topological entropy is lower bounded by the supremum of the Lyapunov exponents of their hyperbolic periodic points in the \emph{unbreakable central subbundle} (i.e., central direction with no dominated splitting) of $f$. The previous result deals with the fact that for $f$ in a residual set $\tilde{\mathcal{R}}$ of symplectic diffeomorphisms (containing $\mathcal{R}$) satisfies a trichotomy: or $f$ is Anosov or $f$ is robustly transitive partially hyperbolic with {\em unbreakable center} of dimension $2m$, $0 < m < d$, or $f$ has totally elliptic periodic points dense on $M$. In the second case, we also show the existence of a sequence of $m$-{\em elliptic} periodic points converging to $M$. Indeed, $\tilde{\mathcal{R}}$ contains an open and dense subset.

math.DS↗
arXiv2012

Non-periodic bifurcation for surface diffeomorphisms

We prove that a "positive probability" subset of the boundary of the set of hyperbolic (Axiom A) surface diffeomorphisms with no cycles $\mathcal{H}$ is constituted by Kupka-Smale diffeomorphisms: all periodic points are hyperbolic and their invariant manifolds intersect transversally. Lack of hyperbolicity arises from the presence of a tangency between a stable manifold and an unstable manifold, one of which is not associated to a periodic point. All these diffeomorphisms that we construct lie on the boundary of the same connected component of $\mathcal{H}$.

math.DS↗