Shuntaro Tomizawa

collaborators

3 papers

math.DS2026

$C^{1}$ -robust strong pluripotency for blender-horseshoes

Teruhiko Soma, Shuntaro Tomizawa

Suppose that $M$ is a closed manifold of dimension greater than two. We show that there exists a $C^{1}$ -diffeomorphism $f_{0} : M ⟶ M$ with a wild affine blender-horseshoe…

math.DS2026

Infinitely Many Attracting Periodic Circles in Higher Dimensions

Shuntaro Tomizawa

We study $C^{r}$ ( $5 \leq r \leq \infty$ ) diffeomorphisms on closed manifolds of dimension at least three with a heteroclinic cycle between two hyperbolic periodic points. At each poin…

math.DS2025

Heterodimensional cycles derived from homoclinic tangencies via Hopf bifurcations

Shuntaro Tomizawa

We analyze three-dimensional $C^{r}$ diffeomorphisms ( $r \geq 5$ ) exhibiting a quadratic focus-saddle homoclinic tangency whose multipliers satisfy $∣ λγ ∣ = 1$ . For a proper three-par…

C1-robust strong pluripotency for blender-horseshoes

Infinitely Many Attracting Periodic Circles in Higher Dimensions

Heterodimensional cycles derived from homoclinic tangencies via Hopf bifurcations

$C^{1}$ -robust strong pluripotency for blender-horseshoes