One-Dimensional Dynamics and High-Dimensional Network Systems

Session

Short Talk

20 Apr 2026, 15:20

Aula Dini (Palazzo del Castelletto)

Conveners

Short Talk: The Arti-Mazur zeta function for interval maps.

• Jorge Olivares-Vinales (SCMS, Fudan University)

Short Talk: Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point

• Rubio Gunawan The (SISSA)

Short Talk: Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$

• Alden Paige (The University of Manchester)

Short Talk: High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphisms

• Dmitrii Mints (Imperial College London)

Short Talk: A Tensorization Approach to Overcoming the Curse of Dimensionality in High-Dimensional Coupled Systems

• Giuseppe Tenaglia (Imperial college London)

Short Talk: Adiabatic invariant actions for partially integrable systems

• Amir Khodaeian Karim (Imperial College London)

Short Talk: Reconstructing resonant phase oscillator interactions from noisy time series

• Bengi Dönmez (Vrije Universiteit Amsterdam)

Short Talk: A counterexample to Hölder regularity of the stationary measure for random noninvertible maps.

• Vincent Goverse (Imperial College London)

Short Talk: Non-statistical skew products with one-dimensional fibers

• Raul Steven Rodriguez Chavez (ICTP and PUC-Rio)

39. The Arti-Mazur zeta function for interval maps.

Jorge Olivares-Vinales (SCMS, Fudan University)

21/04/2026, 12:30

In this talk, I will discuss recent work characterizing the rationality of the Artin–Mazur zeta function for unimodal maps. I will then present examples showing that this characterization fails for multimodal maps, and therefore for polynomial maps of higher degree. If time permits, I will also explain how these examples connect to Thurston’s conjecture on the structure of isentropes for...

43. Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point

Rubio Gunawan The (SISSA)

22/04/2026, 12:30

We construct an example of a smooth circle covering map topologically conjugate to the doubling map, such that it has a physical measure supported on a hyperbolic repelling fixed point. By relaxing the smooth condition at a single point, we also construct an example where the basin of the physical measure has full measure. A key technical step is a realization lemma of independent interest,...

40. Dynamics of Solutions to Quadratic Forms on $\mathbb{R}^3$

Alden Paige (The University of Manchester)

22/04/2026, 15:20

It is known that every positive primitive Pythagorean triple can be uniquely express in the form $M_{a_1} \ldots M_{a_n} v$, where each $M_{a_i}$ is one of three specific matrices, and $v$ is either $(3,4,5)^T$ or $(4,3,5)^T$. Motivated by a desire to compute this code for any given triple, Romik presented an ergodic dynamical system on the positive quadrant of the unit circle, and conjugated...

38. High order homoclinic tangencies and universal dynamics for multidimensional diffeomorphism

Dmitrii Mints (Imperial College London)

23/04/2026, 12:30

Our research is aimed at studying the dynamics of smooth multidimensional diffeomorphisms from the Newhouse domain, that is, open regions in the space of maps where systems with homoclinic tangencies are dense. We prove that in the space of smooth and real-analytic multidimensional maps in any neighborhood of a map such that it has a bi-focus periodic orbit whose invariant manifolds are...

42. A Tensorization Approach to Overcoming the Curse of Dimensionality in High- Dimensional Coupled Systems

Giuseppe Tenaglia (Imperial college London)

23/04/2026, 15:20

Perturbations of high-dimensional systems are notoriously delicate: even when their magnitude vanishes with the dimension, their cumulative effect may remain significant due to the curse of dimensionality.
We study a class of uncoupled noisy systems perturbed by the introduction of a hole whose size decreases as the dimension grows. Although the perturbation becomes asymptotically small, its...

37. A counterexample to Hölder regularity of the stationary measure for random noninvertible maps.

Vincent Goverse (Imperial College London)

Gorodetski, Kleptsyn, and Monakov [1] recently proved that for random dynamical systems on compact Riemannian manifolds generated by bi-Lipschitz homeomorphisms, the stationary measure is Hölder regular whenever the maps do not share a common invariant measure. In this talk, we show that this result does not extend to noninvertible, locally Lipschitz maps. We construct an explicit...

44. Adiabatic invariant actions of partially integrable systems

Amir Khodaeian Karim (Imperial college)

We introduce action variables for partially integrable systems. We prove that for slow-fast partially integrable Hamiltonian systems, when the restriction of the Hamiltonian to the common level of the integrals is ergodic, a slow change of parameters creates geometrically defined adiabatic invariants that are integrals of the averaged system. This is in contrast to the absence of ergodcity....

41. Non-statistical skew products with one-dimensional fibers

Raul Steven Rodriguez Chavez (ICTP and PUC-Rio)

We study the occurrence of non-statistical behavior for almost every point in the setting of skew products with one-dimensional fiber dynamics. Under suitable ergodic conditions, we establish that a weak form of the arcsine law leads to the non-convergence of Birkhoff averages along almost every orbit. As an application, we show that this phenomenon occurs for one-step skew product maps over a...

47. Reconstructing resonant phase oscillator interactions from noisy time series

Bengi Dönmez (Vrije Universiteit Amsterdam)

We present a novel method for reconstructing networks and hypernetworks of coupled phase oscillators from noisy time series. Noise and uncertainty can make it hard or impossible to distinguish different oscillator networks based on observed dynamical behavior. Thus, our method does not aim to determine exact phase equations for the oscillators, but instead recovers their first and second order...