Open problems in Mathematics stemming from research papers

Real Hénon maps (by P. Berger)

Question 1: Can we find a Hénon map (of some degree) which admits a wild attractor, i.e., a Cantor set which attracts a set of Lebesgue positive measure and which is strictly included in a transitive set ?

Refer to Van Strien (2010) who asked whether a suitable analog of wild attractors could exist for Hénon maps (of some degree). ...
- Eric Bedford,
- Pierre Berger,
- Fabrizio Bianchi,
- Xavier Buff,
- Sylvain Crovisier,
- Tien-Cuong Dinh,
- Romain Dujardin,
- Charles Favre,
- Tanya Firsova,
- Patrick Ingram,
- Yutaka Ishii,
- Liviana Palmisano,
- Enrique Pujals,
- Jasmin Raissy,
- Sonja Štimac,
- Gabriel Vigny
Open
Posted online: 2024-03-18 19:41:03Z by SciLag Admin50

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- Dynamical Systems
Collatz Problem

The Collatz conjecture is among the most renowned unsolved problems in mathematics. It postulates whether iteratively applying two elementary arithmetic operations will inevitably lead every positive integer to 1.

It revolves around sequences of integers where each term is derived from the preceding one by the following rules: ...
- E.F.,
- O'Connor,
- J.J.; Robertson
Open
Posted online: 2024-03-18 07:48:00Z by SciLag Admin72
- Number Theory
The Happy Ending problem (forcing convex polygons)

The happy ending problem, is concerned with determining, for $ n \geq 3 $, the smallest number of points in the plane, each in general position (i.e., not collinear), such that any arrangement of these points will always include at least one set of $ n $ points forming the vertices of a convex polygon with $ n $ sides. ...
- Paul Hoffman
OpenYear of origin: 1998
Posted online: 2024-03-18 06:37:40Z by SciLag Admin42
- Combinatorics
Birch–Tate conjecture

The conjecture known as the Birch–Tate conjecture within the field of algebraic K-theory, and was jointly proposed by Bryan John Birch and John Tate.

Let $K$ represent a totally real number field, $\zeta_K$ denote the Dedekind zeta function, and $K_2(\mathcal{O}_K)$ be the algebraic $K_2$-group. ...
- John Tate
OpenYear of origin: 1971
Posted online: 2024-03-18 06:37:43Z by SciLag Admin78
- Algebraic Geometry
- Algebraic Topology
Goldbach's conjecture

Goldbach's original conjecture, referred to as the "ternary" Goldbach conjecture, was communicated in a letter to Euler on June 7, 1742. [1]. It suggests that:

Every number greater than 2 can be expressed as the sum of three primes. ...
- Christian Goldbach
Open
Posted online: 2024-03-15 17:32:42Z by SciLag Admin46
- Number Theory
Riemannian two-sphere contains two smoothly immersed curves ...

The text below is excerpted from [1], with minor modifications in wording.

Birkhoff's celebrated theorem states that any two-sphere equipped with a Riemannian metric invariably harbors a closed geodesic. An enduring puzzle posed by V.I. Arnold in 1981 [2] is as follows: ...
- V. I. Arnold
Open
Posted online: 2024-03-15 16:04:48Z by SciLag Admin48
- Differential Geometry
Projective self-duals

Consider a vector space $V$. The projective space $\mathbb{P}$ consists of all 1-dimensional subspaces of $V$. The projective dual space $\mathbb{P}^*$ is obtained by projectivizing $V^*$, where $V^*$ denotes the vector space containing all linear functions over $V$. For every subspace $A$ in $V$, we can associate its annihilator $A^*$ in $V^*$. ...
- V. I. Arnold,
- Ana Chavez-Caliz
OpenYear of origin: 2023
Posted online: 2024-03-15 15:59:01Z by SciLag Admin28
- Algebraic Geometry
- Geometric Topology

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