Zobrazeno 1 - 10
of 143
pro vyhledávání: '"Yang, Jiagang"'
Let $\mathscr{X}^r(M)$ be the set of $C^r$ vector fields on a boundaryless compact Riemannian manifold $M$. Given a vector field $X_0\in\mathscr{X}^r(M)$ and a compact invariant set $\Gamma$ of $X_0$, we consider the closed subset $\mathscr{X}^r(M,\G
Externí odkaz:
http://arxiv.org/abs/2411.03629
For a class of robustly transitive diffeomorphisms on $\mathbb T^4$ introduced by Shub in [24], satisfying an additional bunching condition, we show that there exits a $C^2$ open and $C^r$ dense subset $\mathcal U^r$, $2\leq r\leq\infty$, such that a
Externí odkaz:
http://arxiv.org/abs/2303.17775
We consider a DA-type surgery of the famous Lorenz attractor in dimension 4. This kind of surgeries have been firstly used by Smale [S] and Ma\~n\'e [M1] to give important examples in the study of partially hyperbolic systems. Our construction gives
Externí odkaz:
http://arxiv.org/abs/2302.02098
For an expanding (unstable) foliation of a diffeomorphism, we use a natural dynamical averaging to construct transverse measures, which we call \emph{maximal}, describing the statistics of how the iterates of a given leaf intersect the cross-sections
Externí odkaz:
http://arxiv.org/abs/2212.05172
It has long been conjectured that the classical Lorenz attractor supports a unique measure of maximal entropy. In this article, we give a positive answer to this conjecture and its higher-dimensional counterpart by considering the uniqueness of equil
Externí odkaz:
http://arxiv.org/abs/2209.10784
We show that for a $C^1$ generic vector field $X$ away from homoclinic tangencies, a nontrivial Lyapunov stable chain recurrence class is a homoclinic class. The proof uses an argument with $C^2$ vector fields approaching $X$ in $C^1$ topology, with
Externí odkaz:
http://arxiv.org/abs/2202.09742
In this note, we consider the thermodynamic formalism for Lorenz attractors of flows in any dimension. Under a mild condition on the H\"older continuous potential function $\phi$, we prove that for an open and dense subset of $C^1$ vector fields, eve
Externí odkaz:
http://arxiv.org/abs/2201.06622
We consider the uniqueness of equilibrium states for dynamical systems that satisfy certain weak, non-uniform versions of specification, expansivity, and the Bowen property at a fixed scale. Following Climenhaga-Thompson's approach which was original
Externí odkaz:
http://arxiv.org/abs/2201.06568
We show that non-trivial chain recurrent classes for generic $C^1$ star flows satisfy a dichotomy: either they have zero topological entropy, or they must be isolated. Moreover, chain recurrent classes for generic star flows with zero entropy must be
Externí odkaz:
http://arxiv.org/abs/2101.09480
We construct measures of maximal $u$-entropy for any partially hyperbolic diffeomorphism that factors over an Anosov torus automorphism and has mostly contracting center direction. The space of such measures has a finite dimension, and its extreme po
Externí odkaz:
http://arxiv.org/abs/2011.02637